"engages himself in" is a correct and usable phrase in written English.
You can use it to describe someone who enthusiastically and actively participates in something, or when a person is actively and devotedly involved in something. For example: "John engages himself in various charitable causes every month, donating his time, energy, and money."
Discussing this and other technologies with an enthusiast's detailed passion, he engages himself in a great deal more.
(7:18) Why did you not simply say something to this effect: he is the sort of man who forgets to eat when he engages himself in vigorous pursuit of learning, who is so full of joy that he forgets his worries, and who does not notice that old age is coming on?
When one of his students reportedly had difficulty describing him, Confucius came to his aid: Why did you not simply say something to this effect: he is the sort of man who forgets to eat when he engages himself in vigorous pursuit of learning, who is so full of joy that he forgets his worries, and who does not notice that old age is coming on?
Mr. da Silva "totally engaged himself in Dilma's campaign and was able to transfer his approval rating, votes and charisma".
Sam was a quiet scholar all his life engaging himself in biomedical research and developments in medical technology.
One boy leaned forward into the circle, trying to engage himself in the lesson, in the way that little children do.
In 1677 he opened a small study hall called the Nanshufang in the Forbidden City, where he engaged himself in lively discussions on philosophical and historical topics with the leading scholars of his time.
There are three areas for a buff to engage himself in: the yard, where the trains are assembled; the tracks; and the switching yard, where empty freight cars are exchanged for full ones.
But if he wants to do more than cast blame, and if trade is as high a priority as he asserts, he needs to engage himself in the struggle for an acceptable compromise.
He particularly engaged himself in offering questions and advice to Jonathan Miller, the newly named chairman of the AOL division, charged with building a new strategy for the online service.
In case of a negative response, the search session is concluded and the participant can either return to the service to engage himself in another session, or abandon the service.
