Rose played college soccer at UCLA between 2008 and 2011. During his time at UCLA, Rose was named All-Pac-10 Conference First Team in both 2010 and 2011. During his time at college, Rose also appeared for USL Premier Development League clubs Seattle Wolves in 2009 and Ventura County Fusion in 2010 and 2011.

On 13 March 2012, the Sounders signed Rose to a professional contract. On 5 May, Rose made his début for the Sounders in a 1–0 home win over the Philadelphia Union. Rose was ranked 24th among MLS players under the age of 24 in 2012, according to MLSSoccer.com.

Rose received his U.S. green card in 2013 which qualifies him as a domestic player for MLS roster purposes. Rose is a UEFA ‘A’ License and UEFA Elite Youth ‘A’ License holder.

In December 2015, Rose agreed a deal with Coventry City to join the English club in January 2016, signing a contract until June 2017.

In 2016, he married Ryan Bradley, the younger daughter of former United States men’s national soccer team and current Los Angeles FC manager Bob Bradley.

On 13 June 2017, Rose signed an initial one-year contract with Scottish Premiership side Motherwell. On 16 May 2018, Rose signed a new one-year contract with Motherwell.

On 10 December 2018, Vancouver Whitecaps FC acquired the rights to Rose from Seattle in exchange for $50,000 of General Allocation Money. He signed with the club on the same day ahead of their 2019 season, with the transfer due to be completed on 1 January 2019.