The Washington Post estimates that around half a million Iraqis are still in Syria as refugees, and as we know, millions of Syrians are now displaced too.
And Iraq is in a state of turmoil, so while Syrians are fleeing to Iraq, Iraqis are fleeing to Syria.
"Between last summer and the first months of this year, about 70,000 Iraqis headed back home (from Syria), according to the United Nations High Commissioner for Refugees. In roughly the same period, as violence has flared in Iraq, about 41,000 Iraqis entered Syria.
The numbers indicate a seesaw movement of people caught between two countries wracked by vicious sectarian wars that are increasingly spilling over their borders."
http://articles.washingtonpost.com/2013-04-10/world/38415037_1_syria-refugees-damascus