Yes. Uvasaggaharam Stotra can be recited at night. Traditionally it is regarded as auspicious to recite in the early morning or in the evening, but it can be chanted at any time when needed, including during the night, especially if you are seeking protection from obstacles or difficulties. Before starting, take a vow ( sankalp ) in your mind and recite with devotion.

You can read more about the proper recitation and timings here