The contract is worth US$700,000 in the NHL. Shore, from Ajax, Ont., recently attended Oilers training camp on a professional tryout.
The 26-year-old shore split the 2019-20 season with the Anaheim Ducks and Columbus Blue Jackets, appearing in 45 games and registering 12 points (five goals, seven assists), eight penalty minutes and a minus-10 plus/minus rating.
The six-foot-one, 206-pound forward was selected in the second round, 61st overall, by the Dallas Stars at the 2012 NHL draft.
He has 39 goals, 67 assists and 49 penalty minutes over 288 career games with Dallas, Anaheim and Columbus.