Can fasting delay my period

Not likely: Likely only if a prolonged fast.

Yes, it's possible.: Reasons for missed/late periods: low body weight, obesity, marked weight ^ or v, over-exercise, endurance athletics, breast-feeding, ^ stress, illness, eating disorders (bulimia or anorexia), anovulatory cycle (no egg released), travel, hormone irregularities, drug use, meds (i.e., birth control) or medical problems. #1 reason is pregnancy.