This question is hard to answer out of context - meaning that I would need to know some of the notes before and after the A# in the melody. Often, a melody implies a tonal center and can be harmonized in context.
That being said, here are some possibilities for your A#:
A# as the root:
Bflat, D F - notice the respelling - Bflat major
Bflat Dflat and F - Bflat minor. Either chord is playable as a barre chord or a partially strummed chord.
A# as the third:
F# A# C# chord - F# major. Playable as a barre chord
G Bflat D - G minor
A# as the fifth:
Eflat, G Bflat - Eflat major chord - easier to spell that way, but difficult to play without barre
Eflat Gflat Bflat - Eflat minor chord.
THEN there are uses for A# as the seventh or ninth of a chord - I would need context from the rest of the melody to answer more fully.
Best wishes on this work, and feel free to send me a midi of the melody, and I'll help you break it down. Even a text listing of the other notes would help.