Both are correct, with "one half" probably predominating in formal writing, and "half" predominating in speech and informal writing. Why this is correct is not precisely clear to me, except that informal speech often does not follow the same "rules" as formal speech.
A sabbatical leave may be granted for the individual’s entire appointment period or for one-half this period, the appointment period being...
The Service Scholars Program provides 24 students each year with scholarship awards equal to one-half of the total yearly cost of Fisher's tuition, fees, and ...
Training plans for running your first or fastest half marathon.
With the information from this book, you can learn to speak English in half of the time it normally takes.
In speech, one often does not use "one/a" before half:
I'll be there in half an hour.
I don't know half these people.