Bickford was the only player among the 33 first-round picks not to sign by Friday's 5 p.m. deadline. The right-hander, who starred at Oaks Christian High School in California, will apparently continue his career at Cal State Fullerton.
His pick had a slot value of $2,921,400, and the figure is deducted from Toronto's signing bonus pool because he didn't reach an agreement.
The Blue Jays will get the No. 11 pick in next year's draft as compensation.
Bickford turned 18 on Wednesday. The 6-foot-4, 185-pounder has a fastball that has been clocked at 97 mph.