A screw that measures .160 diameter is a number 8.
The number 8 comes in two thread pitches, a 32 threads per inch (national course) and a 36 threads per inch (national fine).
Before you buy a tap, take the screw with you and either have the salesperson measure the pitch for you, or just go to the drawers where the nuts are stored and try to screw your screw into one of the nuts.
If it came with the sight, it is probably a 36 pitch thread.
Oddly, both of the number 8 screw sizes use the same tap drill. A number 29 (.1360 diameter) is recommended.