No problem if you reserve in advance.
There is parking but limited but well worth going
We did not have a car. Parking seemed difficult in Oxford. I think the hotel has some parking available.
a good but tight carpark at the right aside of the hotel.
As previous review says parking is limited. When we arrived there was a parking space with our name on it. Just ring the hotel to confirm your booking and car space.
Parking is limited as this is central Oxford. Oxford is very anti car.
However the hotel have maybe 10 or so parking spaces.
If you ask they will reserve one for you. Be aware that restaurant guests will also want to use them. Outside working hours you can always park on a road near by if they are full.
Get an answer from Old Parsonage Hotel staff and past guests.