McKeown started his career as a youth-team player for Ipswich Town. McKeown went on to develop in the Ipswich under-18s and reserve teams before he was released in June 2011 after "Blues" manager Paul Jewell opted not to give him a professional contract upon the expiry of his academy scholarship. McKeown joined Kilmarnock after a short trial in July 2011, having been signed ahead of fellow trialist Mitchell Piqué. Manager Kenny Shiels said that "Rory played for me at 13 as an outside left in my Excellence Programme back in Northern Ireland. I've always seen the potential in him and he's one we can develop into a good left-back". McKeown scored on his competitive debut for "Killie" with "a stunning 25-yard strike" in a 1–1 draw with Dundee United at Tannadice Park on 24 July. However he struggled for first-team action after Jeroen Tesselaar was instead favoured at left-back. He made 21 appearances throughout the 2011–12 season and 18 appearances in the 2012–13 campaign as Kilmarnock posted ninth-place finishes in the Scottish Premier League. On 20 February 2014, McKeown joined Scottish Championship side Cowdenbeath on a one-month emergency loan. He made his debut for the "Miners" two days later and scored 33 minutes into a 2–0 win over Dundee at Central Park. Having made six appearance and scoring once, his loan spell with Cowdenbeath was extended until the end of the 2013–14 season. He featured a total of 16 times for Jimmy Nicholl's "Blue Brazil", scoring two goals, as Cowdenbeath finished in ninth-place but avoided relegation with a 4–1 victory over Dunfermline Athletic in the play-off final. He was released by Kilmarnock manager Allan Johnston upon his return to Rugby Park.
Raith Rovers
On 23 June 2014, McKeown joined Scottish Championship side Raith Rovers. He was an ever-present throughout the 2014–15 season, helping Grant Murray's Rovers to a sixth-place finish. He was also a near ever-present under new manager Ray McKinnon for the 2015–16 season, missing just one Scottish Challenge Cup game. Rovers secured a play-off place with a fourth-place finish, but were eliminated at the quarter-final stage following a 2–1 aggregate defeat to Hibernian.
McKeown joined Northern Premier League Premier Division club Warrington Town in November 2016. On 31 December 2016, he joined National League relegation strugglers Southport. He scored three goals in 19 appearances for Andy Preece's side, who ended the 2016–17 campaign in the relegation places, and he departed Haig Avenuein the summer. On 7 August 2017, he re-signed with Warrington Town. Manager Paul Carden said that "Rory has had opportunities to go in at clubs higher up, but things haven't materialised for him. He's got quality and now he just needs to get his head down. Chances will come to him if he's performing well, everyone is getting watched all the time." He was an ever-present throughout the 2017–18 season to help the "Yellows" to qualify for the play-offs with a third-place finish, scoring the winning goal over Shaw Lane on the final day of the season, but was suspended for the play-off semi-final defeat to Grantham Town after being sent off in the game against Shaw Lane for an "innocuous-looking challenge". He joined Port Vale on trial in July 2018. Manager Neil Aspin said that "he gave a good account of himself" but decided to strengthen in other positions instead.
McKeown is a versatile player, able to play at as a left-sided full-back, wing-back or winger. He has been described as an "athletic modern day left-back", with the extra attributes of pace and a good long-throw.
