THE SHORT ANSWER
Potentially, if both the sponsor and the person being sponsored meet the applicable requirements. A relationship alone does not establish eligibility.
Who needs to meet the requirements?
Both people do. Review sponsor eligibility, the relationship category and the requirements for the person being sponsored. Your residence, status and family circumstances affect the review.
Are marriage and common-law sponsorship the same?
They are different relationship categories with different evidence requirements. Use the official guide and document checklist for your circumstances instead of treating the categories as interchangeable.
Where should we start?
Organize a relationship timeline and identify the relevant application route and checklist. Gather consistent evidence of your relationship and immigration history; disclose previous applications and refusals accurately.
Go straight to the source.
Confirm the current instructions with IRCC before applying. These links are official Government of Canada resources.