The Canadian Civil Rights Movement and the American Civil Rights Movement were quite similar, although Canada remained a part of the empire for significantly longer so many variations lie within Canada's connection to Great Britain. Specifically, Canada abolished slavery when the Empire abolished slavery (1833). The early abolition of slavery in Canada made it a beacon for freedom for many people, seen in the development of the Underground Railroad; however, this downplays Canada's significant history of slavery and continued racial prejudice. In fact, Canada has quite a variety of racial prejudice, evident with the Jewish population during the Second World War and their immigration, in which we barred majority of Jews from entering until summer of 1948, only allowing in about 13,000 between 1933-48, purely due to racial prejudice (see Irving Abella and Harold Troper, None Is Too Many, 2012).
Now, the Canadian Civil Rights Movement led to the creation of African-Canadian newspapers such as Canadian Negro and The Clarion, groups such as the NSAACP (Nova Scotia Association for the Advancement of Coloured People), SECAA, NCA, among others. Most efforts were local rather than national, largely due to the uneven spread of African Canadians across the country. The American Civil Rights movement was largely influential in the decisions of those fighting in Canada, but was not the cause of the movement, and in fact, some provinces had already introduced anti-discrimination laws by the 1940s. More so, it was the media coverage of the American Civil Rights Movement, international in its reach, whereas the localised movements across Canada had difficulty forming a national plan. This alludes to a transnational impact, in which the cultures and policies of both Canada and America are affecting each other and creating reactions within the nations.
The types of racism African Canadians would experience varied on location. Jim Crow style laws were more common in larger communities of African Canadians, while segregation of schools was legislated against in the mid century in Nova Scotia and Ontario. However, there were no overarching Jim Crow laws that demanded continuous segregation, a stark difference in comparison to the U.S. Much like the activism was localised, so was the racism, dependent entirely on the community it would occur in. Activism also intensified after WWII due to participation of African Canadians in the war. The Canadian Bill of Rights, enacted in 1960, made all individuals equal under the law. Canada also has it's famous activists, Viola Desmond being our Rosa Parks, as she refused to leave a "whites only" area in a theatre in Nova Scotia.
There is significantly more history to the Canadian Civil Rights Movement, especially for Indigenous people, but to answer the question, yes, Canada had a Civil Rights Movement