On 4 July 2012, McGinn signed for Scottish Premier League club Aberdeen on a two-year contract after his deal with Celtic expired.  After his move to Aberdeen, McGinn revealed the club’s aim to challenge his former club Celtic and gain a place in Europe.  McGinn joined up with his teammates as they headed out to Germany for a pre-season tour which included games against Werder Bremen and FC St. Pauli. McGinn scored his first goal for the Dons’ in the friendly against St. Pauli, rounding the goalkeeper after picking up the ball from a poor back pass.

He went on to make his competitive debut for Aberdeen, in an opening day 1–0 defeat away to SPL champions Celtic.  The following weekend, McGinn made his home debut against newly promoted side Ross County.  The game finished 0–0 and also saw McGinn stretchered off towards the end of the game after an accidental collision with veteran defender Grant Munro.  Manager Craig Brown spoke after the game, ruling McGinn out of the Northern Ireland squad that was due to face Finland on 14 August.  The former Scotland manager said: “We can’t tell the length of the recovery period but he will certainly be out in the immediate future.”

After being out for 4 weeks due to an ankle injury, McGinn featured as a substitute in a 1–1 draw with Inverness Caledonian thistle. The next week he came on as a substitute against Motherwell and scored his first competitive goal for the club, helping Aberdeen come back from 1–3 down to draw 3–3. He then went on to score in his next 2 appearances for the Dons. A 2–1 victory at home to Hibernian and helped the Dons come back to beat Kilmarnock 3–1 at Rugby Park. A fortnight later, he scored his thirtieth goal in four matches at Tannadice in a 1–1 draw with Dundee United. On 27 October 2012, McGinn became the first Aberdeen player in 20 years to score in five successive league matches, netting the opening goal in a 2–0 win over Dundee.  The following week, in a 2–1 loss to Ross County in Dingwall, McGinn scored in his sixth straight league match, smashing Duncan Shearer’s record. McGinn headed a late equaliser for Aberdeen in a Scottish Cup tie with Motherwell to level the match and set up a replay at Fir Park.

McGinn then bagged the first hat-trick in his professional career in a convincing 3–1 victory over Dundee at Dens Park, on 29 December 2012; this brought his goal tally to 14 before the turn of the year. He scored a sublime free kick in a 2–2 draw with Dundee United at Pittodrie three days later, his 14th goal in 19 league games. On the last day of the transfer window, McGinn revealed he received a six-figure bid from three clubs in the Championship, which he rebuffed, to return the faith shown in him by Craig Brown.  Later in the 2012–13 season, McGinn impressive display earned him a nomination for PFA Scotland’s player of the year.

On 3 May 2013, McGinn was awarded both Aberdeen Player of the Year and Aberdeen Players’ Player of the Year for the 2012–13 season. On picking up the awards McGinn said: “The fans have been unbelievable towards me and I am very thankful to them for that. To win the award voted for by the fans means that you are doing something right on the park. Thank you to everyone that took the time to vote for me”.  McGinn finished the season with 21 goals in all competitions, 20 of those coming in league matches. On 17 May, McGinn signed a two-year extension to his current contract, tying him to the club until 2016.  After signing a new contract, McGinn insisted that he has unfinished business to do by winning trophies for the club.  At the end of the 2012–13 season, McGinn finished the season, with 21 goals in thirty-nine appearance in all competitions.

In 2013–14 season, McGinn scored his first goals of the season in a 3–1 win over Motherwell, followed up his third goal, in a 2–1 loss against Hearts.  However, McGinn soon sustained an ankle injury during an international game that cause him to missed two games.  McGinn then started being on a goal scoring form when he scored five goals in four games against Partick Thistle, Hearts, Celtic and St Johnstone.  Later in the second half of 2013–14 season, McGinn would play a vital role when he provided a double assist, in a 2–1 win over Celtic, giving their first loss of the season.  A few weeks later, McGinn played the full 120 minutes of normal plus extra time in the Scottish League Cup Final against Inverness Caledonian Thistle which Aberdeen won 4–2 on penalty kicks.  McGinn scored his first league goal in three months, as Aberdeen drew 1–1 with Dundee United.  McGinn scored twice on 30 March 2014, in a 2–0 win over Hibernian.  McGinn then finished 2013–14 season as the top-scorer for the second time in a row with thirteen goals in all competitions.

In 2014–15 season, McGinn scored two goals in the Europa League Qualifier, in a 5–0 win over Daugava Rīga in the first leg, followed up his second, in a 2–1 win over FC Groningen.  On 30 August 2014, McGinn first goal of the season came in a 1–0 win over Partick Thistle.  On 22 December, McGinn signed a contract extension, staying with the Dons until Summer 2017.