James Holmes -- Cops Investigating Sex Site Profile

A man claiming to be James Holmes created a profile on a popular sex website just days before "The Dark Knight Rises" massacre ... in which he described his penis as "short/average" ... and law enforcement sources tell TMZ investigators are now looking at the site to determine its authenticity.

"Holmes" created the profile on AdultFriendFinder.com July 5 -- and included a picture of himself with reddish, orange hair ... just as officials in Aurora, CO said he looked when he was apprehended Friday morning.

"Holmes" -- who used the screen name classicjimbo -- included a cryptic message on the top of the profile which reads, "Will you visit me in prison?"

In his profile, "Holmes" says he's 6'0" and single ... with an athletic body. Note -- the FBI says Holmes is 6'3".

"Holmes" describes himself as a "light/social drinker" ... but in the section where he's asked if he smokes or does drugs, he answered, "I'd prefer not to say."

"Holmes" also noted that he's circumcised.

"Holmes" described himself as a straight man ... and said he was seeking a sexual relationship with "Women, Couples (man and woman), Groups or Couples (2 women)."

"Holmes" also notes that he's interested in "Erotic Chat or Email, Discreet Relationship, 1-on-1 sex or Group sex (3 or more!)"

In the section marked, "Introduction" ... "Holmes" said, "Looking for a fling or casual sex gal. Am a nice guy. Well, as nice enough of a guy who does these sort of shenanigans."

According to the website, "Holmes" last logged in to the site sometime in the past 3 days.

"Holmes" posted 2 different photos of himself -- including one shot in which he is posed in front of an image of a woman while wearing headphones.