I actually do this all the time, I've done this for peoples albums that have recorded tracks to beats that were sold already. So I make a new beat around the acapella that they don't have the tempo to.
What I do, Get the original song with the beat in it, load it in Pro Tools, play it, tap my "tap Tempo" button on the mpc as it plays to get a general area, then I'll actually record the click into pro tools over the orig. beat until i get it right on , usually takes about 5-10 minutes. Works 9 out of 10 times. Then I'll make a generic drum pattern with my new tempo and adjust accordingly, sometimes you have to keep a similar drum pattern for the vocals to sit right. Once I got the tempo locked, I'll record in Pro Tools over the acapella, and mess around live with certain sounds to see what fits nice.
I do this almost every other week for people that want new tracks to old beats, or tracks to beats that were sold already. The song i got on the new Baby Bash album (on J Records) lol, was an acapella remake I didn't have the tempo to, so it's a good idea to start mastering this process!