I'm not aware of an international standard, but 9 feet by 19 feet has been a typical size in the USA for many years. I have a 1980's article concerning parking layout on my website. See "Build Better Parking Areas" at this link
Interesting to note that even though cars have gotten smaller over the years, the increased popularity of SUVs and light trucks keeps recommended parking stall size from shrinking.
I agree with SlideRule about the not seeing an international standard. In the UK IStructE produce a design guide for carparks. In it the recommended car bay dimensions are 2.4m wide by 4.8m long which is quite a bit smaller than what seems to be used in USA. This is one reason for not having an internation standard.
The above dims that i have given are for a mixed use car parks. The IStructE guide increases the bay with to 2.5m for short stay car parks. As each bay will see more vechile movements, there will be an increase in the probability of collisions, thus the increase in width will compensate for this. For long stay car parks the width can be reduced to 2.3m for the opposite reasons.
For disabled bays the width should increase to 3.6m and for parent/child bays 3.2m.
I recommend that you get a hold of this manual if you are going to design a car park as it gives lots of useful info regarding geometry (most economical layouts), and the layout of the structure w.r.t. traffic flows. Plus lots of other things to think about.