Here you need to use the direct relative, "a chuir", because "cé" is the subject of "cuir". All those prepositions in there can be confusing, but when the antecedent is the subject of the relative clause you always use the direct relative.
If you swapped the subject and the object of this sentence around, however ("Who did you persuade to read this book?"), then the antecedent "cé" would be the object of the preposition "ar" (i.e. it would be an indirect object) and you would therefore need to use the indirect relative: "Cé ar chuir tú ina luí air an leabhar seo a léamh?".