The phrase "acquaint him" is correct and usable in written English.
It can be used when you want to inform someone about a person or situation, helping them to become familiar with it.
Example: "I will acquaint him with the new project details during our meeting."
Alternatives: "inform him" or "introduce him".
Even though he didn't particularly seem to mind, she worried that he might get irritated or bored if he kept losing, so she decided to acquaint him with a more advanced level of strategy.
Mr. Perry's visit was meant to acquaint him with voters in this early caucus state, where Mr. Romney, a former Massachusetts governor, took a quarter of the vote in 2008.
His mother, herself an aspiring dancer, had him take part in a variety of cultural activities, particularly Indian and Bengali folk dance, hoping, he said, to acquaint him with their traditions and to channel his boundless energy.
If so, someone might want to acquaint him with No. 96, from "Moonstruck": "Snap out of it!" The reality is that, regardless of who is in charge, Albany has trouble shaking the dysfunction that has long defined it for many New Yorkers.
The slave's partial recognition of equality within society comes from the influence of the "signs and effects of this system [of social interrelations] all about him" (LPPO 114) which acquaint him with certain abstract concepts, and which place him in certain relationships to other members of that society.
Keyes's suggestion to warn Lord Mordaunt was treated by Catesby with derision, when he answered that "he would not for the chamber full of diamonds acquaint him with the secret, for that he knew he could not keep it".
His childhood had acquainted him with isolation and loss.
He also served on the Smithsonian's Board of Regents from 1990 to 1994, an involvement that thoroughly acquainted him with the institution.
His time in the sewers acquainted him with construction work, and before long he was a foreman.
As a child, his visits to relatives in the Tidewater countryside acquainted him with the struggles of rural black people.
It was sailing, on another yacht, Farewell, chartered for a Bank Holiday trip, that acquainted him with the girl who would be his wife.
