Usage of interest as a verb: "I interested them in signing up for camp"

This use of interest as a verb has a Causative/Inchoative sense: 'cause s.o to become interested in s.t'. Almost any word in the English lexicon can be used as a verb, noun, or adjective, in the appropriate context.

You can tell it's causative because it has a human agent subject, and the s.o appearing as indirect object is also the patient subject of (become) interested. This is a standard B-Equi configuration, but it seems to be most comfortable in a subordinate clause, viz:

• I tried to interest them in signing up for camp, but I failed to get any signatures.

Interest can be used a verb and "I interested them in signing up" is grammatically correct. There is nothing odd about it and it is acceptable. One such similar sentence which you would have come across is, "Maths has always interested me" . You can also have a look at this link for more details: https://www.macmillandictionary.com/dictionary/british/interest_2