According to an archived "Morning Edition" story on npr.org from 15 August 2005, there were 138,00 U.S. troops in Iraq at that point. To find more current information, I searched the online New York Times archive for "troop levels in Iraq" and "number of troops in Iraq" and found that it's a difficult number to pin down. As of 18 December 2005 (as reported in "Asking Patience, President Cites Progress in Iraq"), there were 160,000 U.S. troops in Iraq, a spike caused by the elections there. As of 31 January 2006 (in the article "Iraqi Official Says Foreign Forces Could Fall Below 100,000 This Year"), there were 140,000 U.S. troops in Iraq. Finally, on 3 February 2006, I found a story ("$120 Billion More is Sought for Military in War Zones") that reports that there are 130,000 U.S. troops in Iraq.

In short, currently, there are currently anywhere between 130,000 and 140,000 U.S. troops in Iraq.