Can we "wish" to somebody for something just like we "pray" to somebody for something as in "I prayed to god for rain" ?

I often hear people say "I wish to god". Is this usage informal, because I can't find such expressions in dictionaries or grammar books ?
I think that that is a semi-fixed expression, DD. I've only heard it with God, heaven, hell, bloody Jesus, etc- and it is always followed by a 'that'-clause, not 'for...'

'To + noun' here is just an intensifier for 'wish': I wish [to heaven] that I were rich!
Thanks, Mister Micawber.
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Mister Micawberit is always followed by a 'that'-clause, not 'for...'

I disagree on this point; “for...” is, in some cases perfectly OK. The example in the OP is one of them. Also things like “...for inspiration”, “...for guidance”, “...for an idea”, “...for strength (to...)” all fall into this category. “That” is more common, though, I will concede.