Though Robert Downey Jr. refuses to make his own political views public, he was happy to share Tony Stark's presidential pick for 2016 in a recent interview with Howard Stern. While promoting Captain America: Civil War, Downey explained:

I believe Tony [Stark], being a budding feminist, he would say it's time to have some feminine energy in the White House.

He confirmed to Stern that "[Tony Stark] does" back Hillary Clinton. It indeed makes total sense that Hillary would earn the backing of a weapons-manufacturing billionaire.

Sources: Howard Stern