Sometimes whether a word functions as a verb or a noun depends on the context. For example, in the following sentences, whatever comes after "put to" is a noun:
- He told the children the cat was put to sleep.
- The murderer was put to death by lethal injection.
- Their wealth puts to shame even the Rothschilds.
After the verb "to put" another verb can follow, e.g.:
- The killer was put to do this by others.
- The rodents were put to exercise on a wheel.
- The slaves were put to work in the fields.
In your example, the verb "to charge" is used in its transitive sense. So, when someone says, "I put my phone to charge" – charge what? – the sentence makes no sense. On the other hand, "I put my robot to charge the phone" makes sense.
Examples with the intransitive verb "to charge":
- The pimp put his hookers to charge more for anal sex.
- The coach put him to charge his opponent like that.
- The cruel dog trainer put the animal to charge at stray cats.