The 43-year-old, who was born Juan Martinez, is a permanent resident of the U.S. and has lived there since he was two years old.
After he was convicted of crack cocaine possession in 2012, a California immigration judge ruled in August 2014 he should be deported from the U.S.
Martinez said he has appealed that deportation ruling, and thought he would allowed to travel while that appeal is underway.
"I've already travelled. I'm on appeal. Yes, I have a deportation case going on, but while you're on an appeal you still have rights as a legal permanent resident," he told The Early Edition on Friday morning.
"I travelled on appeal last year to Europe, nine countries. I came back in. I did a tour in Canada from Montreal all the way to Calgary and it was no problem."
Martinez has a wife and four children in Los Angeles, all of whom are U.S. citizens.
"My daughter asked me if I'm ever coming back. I told her, 'Yes I am, you just have to pray and be positive. It's just going to take a while," he said.
Vancouver-based immigration lawyer Catherine Sas works with Canadian immigration laws, but said she wasn't surprised Martinez was refused.
"When it comes to criminal records, I've had clients enter Canada many many times and then on the 10th time or the 20th time they have a problem," she said.
Martinez said his lawyer is now filing for a habeas corpus to allow him to re-enter the U.S. to go before a judge. He's hoping that judge upholds his right to stay in the U.S. as a permanent resident.
While Martinez is still in Vancouver, he is receiving support from the local hip hop community.
This Sunday, prominent Vancouver musicians like Chin Injeti, Kyprios and many others are holding a concert at Alexander Gastown to raise money to help pay his legal fees.
U.S. Customs and Border Protection did not respond to the CBC's requests for comment.
To hear the full interview with Juan Martinez, click here.
ALSO ON HUFFPOST: