Yes, It is highly likely Oswald was working for the CIA.
Have you ever heard of the Raleigh call? When Oswald was in the Dallas police station he tried to make a call to a man in Raleigh, NC. That person was a counter-intelligence person.
It is likely when Oswald was a Marine he was recruited by the CIA and was sent to the language school to learn Russian. All of a sudden this patriotic Marine allegedly became a Marxist.
If that was the case, why was he calling his contact in counter intelligence?
http://www.groverproctor.us/jfk/jfk80.html
According to a former CIA director Oswald was working for the Soviets. Krushev wanted JFK dead but killed the hit some time before.
Oswald did it anyway. That’s according to Eastern European intelligence agencies at the time.