Alexander also began playing travel Soccer with the Portage Soccer Club. He then attended Portage Central High School, where he was named NSCAA Adidas Boys High School National Player of the Year and Gatorade National Boys Soccer Player of the Year in 2005, before playing college soccer for the Indiana University Hoosiers from 2006 to 2009. He was named to the Big Ten All-Freshman team in his first year, started all 22 matches and was named to the All-Big Ten first-team and the NSCAA Adidas Great Lakes All-Region second-team as a sophomore and a junior.
Alexander was drafted in the third round (44th overall) of the 2010 MLS Super Draft by FC Dallas. He made his professional debut on March 27, 2010, in Dallas's opening game of the 2010 MLS season against Houston Dynamo. After initially receiving limited time in his first season, Alexander started eleven consecutive matches to close the 2010 season and was a key player during FC Dallas' nineteen game unbeaten streak. In all he would appear in 17 league matches scoring two goals and assisting on three.
Alexander was traded to Portland Timbers on August 19, 2011 after making 22 league appearances during the 2011 campaign for FC Dallas in exchange for Jeremy Hall. In his first full season in Portland, Alexander appeared in 24 league matches and recorded a team leading 6 assists.
On February 11, 2013 Alexander was traded to New York Red Bulls in exchange for allocation money. Alexander was an important player for New York in his first year at the club as he appeared in all 34 league matches and scored 4 goals, helping the club to its first major title the 2013 MLS Supporters' Shield. During the 2014 season Alexander once again appeared in all 34 league matches scoring 2 goals and assisting on 9 others.
On January 27, 2015, Alexander was traded to the Montreal Impact alongside Ambroise Oyongo, an international player roster spot and allocation money for Felipe and the 1st pick in the MLS Allocation Draft. After a season and a half with Montreal, Alexander was traded to the Houston Dynamo in exchange for general and targeted allocation money.
In 2017 he helped the Dynamo make the playoffs for the first time in 3 seasons. Alexander appeared in all 5 of the Dynamo playoff games that season and got an assist on Mauro Manotas's goal that put the Dynamo up 2-1 against his former club the Portland Timbers in the Western Conference Semi Finals.
Alexander was selected by FC Cincinnati in the 2018 MLS Expansion Draft.