Suggest me the best AMD graphics card within $100, for ASUS M5A97 LE Motherboard with AMD 4 GHz AM3+ FX-4300 FX-Series Four-Core Edition FD4300WMHKBOX Processor.
Agreed with Niko and Bassim the 7770 the is the best card on your budget but just in case you didnt know you need a 500w power supply to run those cards (you have not listed the spec on your PSU).
Sapphire Radeon HD 7790
Here you can get the Sapphire Radeon HD 7790 1GB for $112. It's a little over your budget but you don't want anything less than this and you'll be satisfied with this card.