Okay. Me again. I downloaded your audio demo and i 'am not sure if you rather want to do the reverse way by aligning the audio properly to a time signature that fits the best. In this case you should hold your mouse pointer over the bpm display of your reaper until a little tap sign appears. Start your audio track and tap to the main beat. (Imagine a straight kickdrum.) This should give you a nearly fitting bpm count but of course not for the whole track. Now you should watch another tutorial that shows how to align audio transients to the grid. You can use time stretching or cutting. It depends on what kind of audio you use. Here for example if you want to try it with stretch markers.

Otherwise search for drum loop or audio alignment. good luck!