WASHINGTON—LOL. Hillary Rodham Clinton has a tech-savvy sense of humor, and she wants you to know it.

The secretary of state is firmly embracing an Internet parody that purports to show her texting various politicians and celebrities, shooting them down with snappy retorts. Clinton invited the creators of the "Texts from Hillary" Tumblr website to the State Department on Tuesday and shared a laugh with them. And, she even submitted her own fake exchange.

The site has become an Internet sensation since it was launched last week. It is based on photographs of Clinton, wearing sunglasses, surrounded by briefing papers and staring at her Blackberry, aboard a military transport plane flying to Libya in October.

In it, the captions show her launching imaginary witty ripostes at her husband, President Barack Obama, Vice President Joe Biden and others who are all depicted in photos looking at smartphones and distracting Clinton from important work at hand.