If you check the programs listed in the other question regarding the ride-along
Police ride along in LondonPolice ride along in London
there is no restriction documented for foreigners to participate in a ride-along programs. However, it is more likely then not that you might be denied because, while I cannot say for sure about other departments, it is quite likely that you're a subject to the background check such as in the case of California State University, Fullerton or Howard County, MD Police Department.
So given that you don't have a US SSN and an associated driver's license it is more difficult to perform and thus more likely to be denied.