Yes, it is possible for an angel to manifest itself in human form. A word of caution: it is also possible for jinn (Muslims and disbelievers) to manifest themselves as human beings. All such manifestations will be visible to us, but we do not have the capability or the knowledge to differentiate whom among those we see are actual humans, angels, or jinn.
You can refer to these two Islam Q&A articles for more information: Humans seeing angels and prophet in awakened state and Are the jinn able to appear in human form? Can they appear in Ramadan?.
Angels manifested themselves in human form to prophets as, for example, the angels that went to Ibrahim ﷺ to give him tidings about his expected son, Is-hāq, and later on went to Lot and his people to destroy Sodom and Gomorrah:
هَلْ أَتَاكَ حَدِيثُ ضَيْفِ إِبْرَاهِيمَ الْمُكْرَمِينَ إِذْ دَخَلُوا عَلَيْهِ فَقَالُوا سَلَامًا ۖ قَالَ سَلَامٌ قَوْمٌ مُّنكَرُونَ فَرَاغَ إِلَىٰ أَهْلِهِ فَجَاءَ بِعِجْلٍ سَمِينٍ فَقَرَّبَهُ إِلَيْهِمْ قَالَ أَلَا تَأْكُلُونَ فَأَوْجَسَ مِنْهُمْ خِيفَةً ۖ قَالُوا لَا تَخَفْ ۖ وَبَشَّرُوهُ بِغُلَامٍ عَلِيمٍ
Has the story reached you, of the honoured guests [three angels; Jibrael (Gabriel) along with another two] of Ibrahim (Abraham)? When they came in to him, and said, "Salam, (peace be upon you)!" He answered; "Salam, (peace be upon you)," and said: "You are a people unknown to me," Then he turned to his household, so brought out a roasted calf [as the property of Ibrahim (Abraham) was mainly cows]. And placed it near them; he said, "Will you not eat?" And he felt from them apprehension. They said, "Fear not," and gave him good tidings of a learned boy.
— Surat Adh-Dhariyat 51:24-28
Angels manifested themselves in human form to prophets as well as others present with the prophets at the time. For example, the angels that appeared to Lot in the story above; people of Sodom and Gomorrah could see them (as did Sarah, the wife of Ibrahim ﷺ). The companions had a similar experience during the Battle of Uhud when they saw the angels next to the Prophet ﷺ during the battle:
حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا مُحَمَّدُ بْنُ بِشْرٍ، وَأَبُو أُسَامَةَ عَنْ مِسْعَرٍ، عَنْ سَعْدِ بْنِ إِبْرَاهِيمَ، عَنْ أَبِيهِ، عَنْ سَعْدٍ، قَالَ رَأَيْتُ عَنْ يَمِينِ، رَسُولِ اللَّهِ صلى الله عليه وسلم وَعَنْ شِمَالِهِ يَوْمَ أُحُدٍ رَجُلَيْنِ عَلَيْهِمَا ثِيَابُ بَيَاضٍ مَا رَأَيْتُهُمَا قَبْلُ وَلاَ بَعْدُ . يَعْنِي جِبْرِيلَ وَمِيكَائِيلَ عَلَيْهِمَا السَّلاَمُ
Sa'd reported that on the Day of Uhud I saw on the right side of Allah's Messenger (ﷺ) and on his left side two persons dressed in white clothes and whom I did not see before nor after that, and they were Gabriel and Michael (Allah be pleased with both of them).
— Sahih Muslim, Book 43, Hadith 63
A similar experience happened to a high number of companions in the long hadith in Sahih Muslim, Book 1, Hadith 1 about Archangel Jibrīl teaching the companions about Islam, imān, ihsān, and the signs of the Hour. It has also been reported in the Qur'an that angels appeared to people other than prophets and not in the company of prophets:
وَاذْكُرْ فِي الْكِتَابِ مَرْيَمَ إِذِ انتَبَذَتْ مِنْ أَهْلِهَا مَكَانًا شَرْقِيًّا فَاتَّخَذَتْ مِن دُونِهِمْ حِجَابًا فَأَرْسَلْنَا إِلَيْهَا رُوحَنَا فَتَمَثَّلَ لَهَا بَشَرًا سَوِيًّا
And mention in the Book (the Quran, O Muhammad SAW, the story of) Maryam (Mary), when she withdrew in seclusion from her family to a place facing east. She placed a screen (to screen herself) from them; then We sent to her Our Ruh [angel Jibrael (Gabriel)], and he appeared before her in the form of a man in all respects.
— Surat Maryam 19:16-17
Another example is in the hadith in Sahih Muslim, Book 45, Hadith 47 about someone traveling to see his brother for the sake of Allah when an angel appeared to him to give him good tidings.
The disbelievers of Quraish saw the devil manifested in a human form (that of Suraqa bin Malik, who was a disbeliever at the time but embraced Islam at a later stage) as mentioned in the tafsīr of Surat Al-Anfal 8:48. Companions encountered jinn manifested in human form while not in the presence of the Prophet ﷺ as in the story of Abu Huraira (partially quoted below) when he was guarding zakāt al-fitr and a shaitān appeared to him to steal some of the donated food:
قَالَ النَّبِيُّ صلى الله عليه وسلم: صَدَقَكَ وَهْوَ كَذُوبٌ، ذَاكَ شَيْطَانٌ
The Prophet (ﷺ) said, "He told you the truth, though he is a liar, and he (the thief) himself was the Satan."
— Sahih al-Bukhar, Book 59, Hadith 84
Not only devils maay manifest themselves to us, but Muslim jinn may also do so as per the following hadith where potentially both Muslim and disbleivers from the jinn can manifest themselves to us:
عَنْ أَبِي سَعِيدٍ الْخُدْرِيِّ، قَالَ سَمِعْتُهُ قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم: إِنَّ بِالْمَدِينَةِ نَفَرًا مِنَ الْجِنِّ قَدْ أَسْلَمُوا فَمَنْ رَأَى شَيْئًا مِنْ هَذِهِ الْعَوَامِرِ فَلْيُؤْذِنْهُ ثَلاَثًا فَإِنْ بَدَا لَهُ بَعْدُ فَلْيَقْتُلْهُ فَإِنَّهُ شَيْطَانٌ
Abu Sa'id Khudri reported Allah's Messenger having said: There is a group of jinns in Medina who accepted Islam, so he who would see anything from these occupants should warn him three times; and if he appears after that, he should kill him for he is a satan.
— Sahih Muslim, Book 39, Hadith 192
Numerous accounts of prophets encountering jinn, either on their own or in the presence of others, are documented in the Qur'an and ahadith. The common factor to all the stories above is that neither prophets nor ordinary people in any incident could tell that the person(s) they encountered was not a true human, and were only able to tell that they were angels or jinn through revelations, either from the prophets or from the messengers (angels) themselves.