The goalie said his 11-year-old son was the target of vile tweets from "idiots" following Saturday's Scottish Cup defeat.
Simonsen, who replaced an injured Cammy Bell for the semi-final clash against Dundee United, made a mistake which saw his side go 3-1 down.
Yesterday he said was quitting the social network later today after his family were targeted.
In a series of tweets, he told followers: "I've taken the unfortunate decision that as of 5pm tomorrow this account will be deleted, I won't accept mindless abuse of my family and son.
"I understand this spoils things for the thousands of genuine fans & followers out there, but I will not accept the idiots who resort to abusing someone's family and particularly children.
"Thank you to everyone I've interacted with over the years!! Met some wonderful people!"
He added: "My son comes on twitter to follow his heroes including his dad and ends up having idiots abusing him.
"He's 11 years old.
"His first ever trip to Ibrox to watch his dad ends up with him receiving abuse because I included him in a tweet. I'm sorry but I'm not tolerating it!"
Some of Simonsen's 15,400 followers, including Rangers fans, replied with messages of support for the reserve goalie.
Supporters also took to online forums to condemn the abuse.
Simonsen stepped up after Cammy Bell suffered an injury during training rendering him unfit for Saturday's clash.
Earlier in the week Simonsen tweeted his excitement ahead of the game and said: "Feel so sorry for Cammy, it's rotten luck, but I will step up. I want this so much, for me, for my teammates, my kids, and The Rangers Family!"
Meanwhile, Rangers Football Club have today announced a new shirt sponsorship deal with online casino company 32Red.
The firm, who have previously sponsored English Premiership sides Aston Villa and Swansea, will sponsor Rangers for the next three seasons starting from July 2014.
Rangers chief executive, Graham Wallace, said: "We are in the process of rebuilding Rangers Football Club and alliances with blue chip companies such as 32Red will assist us on our journey back to the top of Scottish football.
"We would like to thank our current shirt sponsor Blackthorn and Tennent Caledonian Breweries for their ongoing support of the club during a very difficult period."