There are no comprehensive ships passenger lists of immigrants arriving in Canada prior to 1865. Until that year, shipping companies were not required by the government to keep their passenger manifests. However there are individual Immigration projects and databases online that may be of help in your search for ancestors
The National Archives of Canada (NAC) aka Library & Archives Canada (LAC) holds immigration
records from 1865 to 1935. These are searchable online but from 1865-1922 are not searchable by passenger name. From 1922-1935 the images are searchable by passenger name.
To obtain a copy of your own landing record, you must submit an Application for a Certified True Copy, Correction, or Replacement of an Immigration Document to Citizenship and Immigration Canada
Alternatively, you can apply for a Permanent Resident Card