Per the Rogers' wikipedia page:

> Rogers remained in command of USS Vincennes until May 27, 1989.[13] In 1990, Captain Rogers was awarded the Legion of Merit decoration "for exceptionally meritorious conduct in the performance of outstanding service as commanding officer ... from April 1987 to May 1989." The award was given for his service as the Commanding Officer of Vincennes, and the citation made no mention of the downing of Iran Air 655.[14]

So no, he wasn't given the award for the downing of Iran Air 655.