It's implied, but not confirmed that he lost that part. The evidence is firstly Theon thinks about Ramsay having had removed "that other thing" in addition to his toes and fingers. Then during fake Arya's bedding in ADWD:
Ramsay: "Reek, get over here. Get her ready for me."
Theon: "I ...... do you mean ... m'lord, I have no ..... I ..."
Ramsay: "With your mouth,"
This strongly implies that "thing" was removed. Furthermore, Ramsay tells Theon:
But you’re no lord, are you? Only Reek. Not even a man, truth be told.