Jennifer Aniston sparked rumors she not only has a significant other but that they could be engaged after rocking a gigantic diamond sparkler on that finger at the SAG Awards over the weekend, RadarOnline.com has learned. The Morning Show star, 55, has not gone public with any new romance or been linked to anyone in five years; however, that did not stop the rumor mill from turning when she wore an attention-grabbing dazzler on the red carpet. Aniston — whose past ex-husbands include Brad Pittand Justin Theroux — shined at the Shrine Auditorium & Expo Hall in Los Angeles in a hip-hugging silve…