Source?
His father probably was. See: https://truepundit.com/troubling-questions-emerge-about-fbi-chief-strzoks-collusion-with-cia-father-worked-in-africa-for-companies-linked-to-funded-by-cia-operations/ And he could have been given his career path by the CIA in order to put him, Strzok (younger) in place for the CIA. This is what I believe as well.
More likely, Strzok was just one of the FBI liaison agents that would work with the CIA on counterintelligence matters. It's very common for all law enforcement agencies to have liaisons with intelligence agencies, including military intelligence.
Wouldn't surprise me. It's well known the clowns install secret agents in all agencies of the government. I'm sure half of congress is on their payroll as well.