'acknowledge themselves' is correct and usable in written English.
You can use this phrase to indicate a situation where someone is recognizing and accepting their own qualities or abilities. For example: The participants were asked to acknowledge themselves for their hard work.
"They won't understand it at the complex level, but we can begin the process by teaching them to acknowledge themselves in terms of their cultural-rather than racial-background.
Jones' attempt at laying all this bare begins with a considerable amount of reporting: his undertaking is built upon dozens of interviews with establishment figures, some of whom would acknowledge themselves as such, some of whom wouldn't.
The Russians would acknowledge themselves that a political solution in Syria has to involve the moderate opposition members and yet they are waging a war of attrition against them and killing large numbers of civilians.
But the vast majority readily acknowledge themselves as "data rich and information poor". In these organizations, too few people are involved, too much data can't be trusted, and too much data lies fallow in vast, unexamined warehouses.
Whether they explicitly acknowledge themselves as leaders or not, artists often move others to follow them — into neighborhoods, into a new a social movement, or even just a dialogue.
In 1772 James Whitchurch wrote in his Essay Upon Education that Locke was "an Author, to whom the Learned must ever acknowledge themselves highly indebted, and whose Name can never be mentioned without a secret Veneration, and Respect; his Assertions being the result of intense Thought, strict Enquiry, a clear and penetrating Judgment".
And in a way they're acknowledging themselves.
It also signaled that he and, by extension, the monarch he spoke for acknowledged themselves to be subject to the Ottoman sultan's authority.
It would also give European governments a better chance of weeding out potential bombers – a fact that some Syrian refugees have acknowledged themselves.
Lots of startup founders have come from 9900 in the past but they've never acknowledged themselves as unit vets.
In Africa, one in four men has acknowledged themselves to be perpetrators.
