Canvas does have a Course Audit log API, but according to documentation it will only work if your instance has audit logs configured.
Here's a PowerShell command to get you started:
(Invoke-RestMethod https://yourCanvasInstance.instructure.com/api/v1/audit/course/courses/:course_id -method get -headers @{"Authorization" = "Bearer $auth"}).links
I do not have a test case where I found actual audit logs (I'll have to check if we have this setup), but this is the closest method I can find to automating this.
Edit: You may need to access the "events" attribute, not links
(Invoke-RestMethod https://yourCanvasInstance.instructure.com/api/v1/audit/course/courses/:course_id -method get -headers @{"Authorization" = "Bearer $auth"}).events