Turn away someone and
Turn someone away have the same meaning?
turn away is defined as, according to Merriam Webster:
to refuse admittance or acceptance to
As for each individual form of the phrasal verb, they are synonymous with each other with no difference in terms of meaning. The only discrepancy between the two is how frequently used each of them are.
turn(ing) away someone does indeed exist, though not commonly used.
Example from Merriam Webster:
using tree branches, the campers were able to turn away the charging fox, which was apparently rabid
Example from TheFreeDictionary.com:
Extremely high prices in the area have been turning away would-be homeowners.
turn(ing) someone away is much more widely used, and is what many native speakers prefer.
The hiking real estate prices turn people away.
Example, from Collins Dict.:
Turning refugees away would be an inhumane action.