While attending Harris Academy, Wighton was snapped by Dundee under the management of Barry Smith, the team he supported as a boy. He came through the same training clinic, run by Ian Cathro, as fellow Scottish prospects Ryan Gauld and John Souttar. Wighton revealed he turned down a move to local rivals Dundee United, as his family are Dundee supporters. While growing up, Wighton initially played out wide before joining Dundee, who then moved him into the striker position. Manager John Brown said in March 2013 that if Wighton continued his form at youth level he could soon make the first team, which could have meant him becoming the club's youngest-ever first-team player. His first team debut for the club was delayed due to SPL rules. Despite interest from elsewhere, Wighton signed his first professional contract on his 16th birthday. After signing a professional contract, he left school to concentrate on his football career.
In the 2013–14 season, Wighton made his debut for the club, coming on as a substitute for Craig Beattie in the 81st minute, as Dundee beat Cowdenbeath 2–0 on 5 October 2013. In his second appearance, Wighton set up two goals as Dundee beat Dumbarton 4–1 on 12 October 2013. He then made his first start for the club, as Dundee beat Queen of the South 2–1 on 19 October 2013. He became the youngest-ever scorer in a competitive game for Dundee at the age of 16 years, three months and 13 days on 9 November 2013, beating the record held by Jocky Scott, scoring a goal in a 2–0 win against Raith Rovers. His second goal came on 14 April 2014, when he scored after six minutes, as Dundee beat Cowdenbeath 4–0. Throughout his debut season he regularly contributed in the Dundee first team, making a total of 14 appearances and scoring two goals for the club, in all competitions as Dundee won the Scottish Championship. Throughout the season Wighton was linked with a move to Premier League clubs and Rangers. At the end of the 2013–14 season, the club's manager Paul Hartley said he may consider loaning out Wighton to gain first team experience with the hope he could "do a Stevie May," the striker who Hartley had on loan at Alloa Athletic from St Johnstone in 2011–12 and had gone on to be a first team regular in the Scottish Premiership, earning a move to Sheffield Wednesday.
2014–15
On 16 August 2014, Wighton scored his first Premiership goal as Dundee drew 1–1 with Partick Thistle, although afterwards, Hartley said he didn't want to talk too much about Wighton, but did announce he had signed a new three-year contract. As a result of his performance, the club decided not to send Wighton on loan. On 18 December 2014, Wighton moved on a short-term loan to Brechin City. After making his debut as a substitute he went on to score two in three starting appearances as well as aiding Brechin to a win over local rivals Forfar with a creative flick past the Forfar defence to assist Alan Trouten to his winning goal at Station Park.
2015–16
On 23 June 2015, after much speculation it was finally confirmed that Wighton had joined Raith Rovers on a six-month loan deal. On 3 January 2016, it was confirmed that following Wighton's loan spell at Raith Rovers he had returned to Dundee. Wighton managed to add 2 goals to his name after returning to the club from his loan spell, he came off the bench to score in an empathic 5-2 Victory over Ross County and more noticeably he scored a 93rd minute winning goal in a Dundee derby known as the "Doon Derby", a result which confirmed that rivals Dundee United would be relegated.
2016–17
Wighton signed a three-year contract with Dundee in June 2016. Wighton picked up a Man of the Match award with an impressive performance in a 2-0 Victory over Motherwell having set up both goals. After a frustrating season with the club just avoiding relegation Wighton revealed that his glimpses of quality throughout the season were not good enough as he was determined to show more consistency the season after.
2017–18
After impressing manager Neil McCann in pre-season, Wighton picked up a knee ligament injury which ruled him out for several months. A season which was described to be "Very Crucial" for Wighton's development and career, McCann also went on to say he was "heartbroken" for the youngster due to the situation.
He was dropped from the Hearts first team squad by Daniel Stendel in January 2020, and was then loaned to Arbroath. Wighton scored on his debut with the Lichties in a win over Partick Thistle. After impressing in his short spell for the Lichties with 3 goals in 5 games, Wighton returned to Hearts in May due to the early curtailment of the 2019–20 season due to the COVID-19 pandemic.
Style of Play
His then teammate at Dundee, Gavin Rae said Wighton's playing style reminds him of Aaron Ramsey, who Rae played alongside in his time at Cardiff City. Then assistant ManagerRay Farningham described Wighton as "one of the top young prospects in the Scottish game."
