Would you ever say "have him to call" (emphasis on "to")?

This won't be of much help to you, I think, but the phrase does sound acceptable to me, if not exactly "normal". I would never use this construction myself, but I've obviously heard it used enough for it to sound okay. It feels like more of a Southern style of speech to me. I've spent some time in the South and also read a lot. I'm from the U.S. west coast.

EDIT: Having done a good deal of linguistics coursework in my graduate degrees and having taught ESL students for several years, hearing people attribute this construction to second language learning bothered me enough to get me to do an online search for more information.

Typing in "have him to call" produced several examples of people using the form in their own Internet posts, but the only specific reference to the construction in a linguistic context was this one:

"Also specific to Southern speech is the use of an infinitive verb in conjunction with the word 'have' to produce a sentence akin to 'Shall I have him to call you?'(93)"

That's enough, though, to make me believe that you are on the right track with this. I honestly believe that it's part of a Southern dialect, and with library research, you should probably be able to find more information on it.

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I have lived in the South East part .of the states for years now. I hear this quite a bit.Think of the sentence-I will ask him to call- He may call and he may not but I will ask him to. Then you have the sentence I will have him call- He will call because I WILL HAVE HIM CALL.I will have him to call is only a combination of the two.Not necessarily proper but close enough if you don't want to be real picky. Then again, this is just my opinion

It sounds like either

1) learner-language / inter-language based on interference "translation" of native language of a NNS, say a Spanish speaker literally translating the infinitive

2) archaic speech, 17th thru 19th century English (heard in songs, English or Irish-English, and helps rhythm).

Jamaican creole may also preserve this type of thing, although "to" would be replaced with "fe": "Have him fe clean up him room"

I'm from New England.

In English we usually say "have him call" (without the "to"). It sounds like you are learning English as a second language. For instance, in Spanish it would be proper to use the verb "llamar" or literally, "to call". That is very common in Spanish, however, it may be heard said in English, but it is not accepted as proper grammar.

I just wanted to chime in and say I'd never use the "have him to do something" construction. I'd always say it without the "to". I'm from the US, Pacific Northwest.