Cookson, a 24-year-old centre or second-rower, was found to have provided a sample containing the stimulant methylhexaneamine - the banned substance for which former Great Britain centre Martin Gleeson was handed a three-year ban in 2011, half of which was suspended.
It is a specified substance which appears on the World Anti-Doping prohibited list which means it is susceptible to inadvertent use.
A League spokesman said: "The RFL advise all players to be aware of methylhexaneamine, which has been the cause of a number of positive tests throughout the world.
"All players are advised to assess the risk associated with supplements and to take steps to minimise the risk."
Cookson, a former Great Britain Under-23 amateur international, made 18 appearances for Oldham in 2012.
His suspension was back-dated to August 31, 2012 and ends on February 28.