"persuade him into" is correct and usable in written English.
You can use it when trying to persuade someone into doing or trying something. Example: I tried to persuade him into coming with us to the party.
Once, when Naipaul's legs give out on the long walk to see the bones of ancestors in Gabon, helpful locals persuade him into a wheelbarrow.
Jackets should be Harrington or Bomber in style and hit the waist, or see if you can persuade him into a shrunken-shape jumper or cardigan - worn with a looser trouser, he'll be in perfect proportion.
I must have this, I must have that.'" Brown and the orchestra eventually became so annoyed by Spector's behaviour that the orchestra refused to play any further, and at one point, Brown left for home, forcing Spector to telephone him and persuade him into coming back after Starr had told Spector to calm down.
For example, if you are Atheist or Agnostic, don't try and persuade him into believing God isn't real.
Suddenly, Damascus became a Mecca for all sorts of emissaries, both official and unofficial, from the United States and the European Union seeking to meet with Mish'al in the hope of persuading him into a compromise of some sort to pave the way for lifting sanctions.
The deliberate devastation of the Elector's lands in Bavaria failed to bring Max Emanuel to battle or persuade him back into the Imperial fold.
Earlier efforts to persuade him to go into temporary exile failed, and diplomats involved in the negotiations said his status was put aside to avoid saddling the talks with yet another problem.
It took Ms. Esphahani a year and a half to persuade him to move his operations into Safdico's office on Fifth Avenue, which he did in 2002.
During a Feb. 14 meeting in the Oval Office, the day after the firing of national security adviser Michael Flynn, Comey said Trump tried to persuade him to drop an investigation into Flynn.
This spring Angélica persuaded him to go into detox.
A bishop in his home region persuaded him to go into politics.
