What is the word for someone who checks ID cards before permitting entry?

Doorman : http://en.wikipedia.org/wiki/Doorman

Wordnet 3.0 says:

2. gatekeeper - someone who guards an entrance
doorman, hall porter, door guard, ostiary, porter, doorkeeper
commissionaire - a uniformed doorman
guard - a person who keeps watch over something or someone
night porter - a porter on duty during the night
ticket collector, ticket taker - someone who is paid to admit only those who have purchased tickets

“Doorman” is good, but makes me (and Google) think you mean one of these guys:

In your scenario, I would describe that person and/or those working with him in similar functions collectively or individually as (the embodiment of) security.

“Have you seen any vehicles or other visitors in the vicinity in recent weeks?”

[. . . .]

“I'll check with security but I don't think so.”

_{Source: The Whisper of Legends: An Inspector Green Mystery, By Barbara Fradkin}

Other examples of this usage here.

It’s definitely a more general term, but in your context (or any of minimal specificity) a nice general term like this one can be very clear where an incorrectly specific term would sound strange.