The correct answer is: to.
The preposition “to” is used to indicate a state of being addicted to something. For example, “He became addicted to drugs.”
The preposition “for” is used to indicate a period of time during which someone is addicted to something. For example, “He was addicted to drugs for many years.”
The preposition “by” is used to indicate the means by which someone becomes addicted to something. For example, “He became addicted to drugs by experimenting with them.”
The preposition “into” is used to indicate a change in state, such as from being not addicted to being addicted. For example, “He fell into drug addiction.”
In this case, the preposition “to” is the most appropriate choice because it indicates that the man was in a state of being addicted to drugs.