The 20-year-old has been capped by his country nine times and was a free agent following his release from Wolverhampton Wanderers where he made one Premier League appearance in March 2012.
Gorman scored in the 4-4 draw against Arsenal XI on Tuesday night and having also seen him figure in the training match against QPR last weekend, Orient manager Russell Slade believes he has seen enough to reward him with a contract.
“Johnny has impressed me in the couple of performances he’s put in for us. He’s got good pedigree and a very strong left foot. I think we will see him play an ever-increasing part as the season goes on,” said Slade.
Gorman will wear the number 20 for the O’s.