The 21-year-old former Everton youth player tested positive for the anabolic steroid Nandrolone, which he claims he took for pain relief following a recommendation from his cousin
The 21-year-old, who was a trainee at Everton earlier in his career, admitted a Football Association charge of breaching anti-doping regulations after supplying a urine sample containing the anabolic steroid Nandrolone.
Kinsella will now be banned from football until 2015, subject to an appeal.
The midfielder claims to have taken the drug for pain relief following a recommendation from his cousin, but the FA determined that Kinsella "made no proper efforts to establish what the substance was and whether it was prohibited."
He has yet to make a full appearance for the League Two club, having spent time on loan at Telford last season. Kinsella's deal at Highbury expires next summer.