Born in Newry, County Down, McGivern is a product of the Manchester City youth teams.
Discovered by highly rated former scout Willie McKeown, McGivern played in their 2008 FA Youth Cup final win over Chelsea.
He was also in the side that lost to Aston Villa in the play-offs final of the 2007–08 Premier Academy League and had scored in the semifinal win over Sunderland.
McGivern was promoted to City's first team squad for their Premier League game versus Fulham on 12 April 2009 and was an unused substitute.
He made his first team debut in a Premier League game against Sunderland on 3 April 2011, coming on as a substitute in the 70th minute to replace Dedryck Boyata in a game that City won 5–0.
On 25 October 2008, it was announced that McGivern would be joining Morecambe on loan until the New Year. Morecambe, who were managed by former Northern Ireland player and manager Sammy McIlroy who stated that "I have seen Ryan play a few times and been very impressed by what I've seen".
He scored his first ever senior goal during a game with Aldershot on November 1.
On 29 August 2009, McGivern joined Leicester City on loan until January 2010.
He made his debut in a 2–0 win over Crystal Palace on 20 October 2009, scoring an own goal in a 1–1 draw against Ipswich Town on 10 January 2010.
McGivern's loan was extended until the end of the season on 11 January.[8] He played a total of twelve league games for Leicester but was not selected for the Championship play-off semi-finals, which they lost to Cardiff City.
McGivern was loaned to Walsall on a season long loan for the 2010–11 season, having won the race from other club,[11] but was recalled on 20 January 2011 six month later.
After signing a new deal, keeping him until 2013, McGivern made a 28-day loan move to Crystal Palace on 3 August 2011, providing an assist for Jonathan Parr on his home debut for the Eagles. After his loan spell at Palace ended, McGivern moved to Bristol City for the remainder of the 2011–12 season. He made his debut for Bristol City on 10 September, against Brighton & Hove Albion.
McGivern signed on loan for Scottish Premier League side Hibernian until January 2013. Having been on the unused substitute for two games, McGivern finally made his debut, coming on for Alan Maybury, in a 2-1 loss against Aberdeen.
He since established himself at Hibs, playing in the left-back position, replacing Maybury, who would play in the right-back position.
After a successful loan spell, McGivern agreed a permanent deal with Hibernian after his contract with Manchester City came to an end.
The defender signed a two year contract with the Easter Road side