I think the word you are looking for is 'framed'. 'The cop framed Jack on drug charges'. Or another phrase is 'trumped up charges'. 'The cop laid trumped up drug charges on Jack'.

'to fit up' "I was just standing outside the shop, but the cops fitted me up for drugs by dropping a bag of weed in my pack."

I can't think of an actual verb for that, but it is useful to think about the collocations within the context you described. You could say, the cop laid charges on Jack for doing drugs. Another collocation is to press charges. Jack was arrested for doing drugs. Police will press charges. Cop is a very informal word and so you could use a phrasal verb in this instance- Jack was had up by the cops for doing drugs.