If you check the programs listed in the other question regarding the ride-along

http://travel.stackexchange.com/questions/27842/police-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][1] or [Howard County, MD Police Department][2].

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.

[1]: http://police.fullerton.edu/policeservice/RideAlong.asp
[2]: www.co.ho.md.us/WorkArea/DownloadAsset.aspx?id=6442451238