Does the FAA prescribe radar cross-section requirements for civilian aircraft?
No. Primary radar isn't a universal tool to begin with. Secondary radar and thus transponders are more commonly used. So there are regulations as to where and which aircraft need to install transponders. Ultralights and some GA can get away without.

Related: Is it legal to make a non-military stealth plane?

No RCS requirement, but you'll need a transponder regardless.