6 seasons of arbitration.
Look at how many seasons he's served (its near the top right of his player's page)
After 3 full seasons, he'll eligible for arbitration for the first time. After 4 seasons, he'll likely ask for more in arbitration (scrubs who don't play much often ask for just the minimum), after 5 seasons he'll ask for the largest amount in arbitration. After 6 ML seasons, he's eligible for free agency, though you can look him up to a long term deal prior to that. Important to note, that its ML service time, not professional service time. Some guys will spend 4 seasons in the majors, then the rest of their career in the minors. They'll come up for arbitraiton each season that you keep them on the 40 man roster, but they won't accure ML service time if they're playing in the minors.