was this new when you bought it?
ok, so you can get RCA ends and a small spade lug and terminate the cable coming out of the turntable. If its not long enough to reach your amp then I would advise replacing it rather than splicing it with the other cable you found.
You can splice the two cables together if you want, your call but I wouldn't. I'm guessing the wires ends were just twisted together before...?