Angus publicly quit using the microblogging site earlier this year, likening it to being badgered by a drunk on a 24-hour bus ride.
But he says that a House of Commons study on privacy and social media requires the company's input.
A Commons committee decided last May to study the steps being taken by social media companies to protect the personal information of Canadians.
It followed high-profile interventions by Canada's privacy commissioner on the use of personal data by sites like Google and Facebook.
Both companies have appeared before the committee, but NDP MP Charmaine Borg says Twitter refused.
The company couldn't immediately be reached for comment.
The committee has now agreed to send a formal letter asking Twitter to testify.
Angus said Google and Facebook has supported the study, but the committee needs to go further.
"We're not going to have a full sense unless we have the main players," said Angus. "We need Twitter."
The motion to formally call Twitter to testify came after a representative from Facebook took committee members through that company's privacy policies.
Facebook's relationship with Canada's privacy commissioner is robust, said Robert Sherman, manager of privacy and public policy for the social networking giant.
"We found that we have had a very positive relationship with her office and have been able to discuss many of the issues and products that we've been coming out with her office and get their feedback," Sherman said.
"That's been a very positive relationship and I think you'll see that many of the innovations around privacy have come out of our discussions with her."
Canadians are heavy users of social media.
A Paris-based analyst group reported in July that there are just over 10 million Twitter accounts based in Canada.
Another analytics company said earlier this year that Facebook has about 18 million Canadian users, more than half the country's total population.Suggest a correction