According to this site:
Tourists are no longer allowed to rent motorcycles or cars, or drive a vehicle in Siem Reap.
I have read several blog posts about Angkor Wat and that's the first time I have read this. Currently, is it true?
No, you cannot do this any more.
The reason is that the Angkor Wat archaeological park is a protected complex, and drivers need to be registered with the authorities who maintain the park to be allowed into it. My tuk-tuk driver told me they need to be registered too, and of course, any tourists need to buy a valid pass. I am guessing that people who live in the area have some sort of residence permit or pass, but I did not see tourists themselves driving around on motorbikes.
The temples themselves are very far apart and it's a big trek to cover them on foot. I'd advise keeping the tuk-tuk with you. It doesn't cost more than $15-20 a day.
What is still possible for tourists is to rent bicycles (basic ones go for $2-3/day, mountain bikes for $5-8).
Given the terrain (completely flat, pretty good roads, mostly shady) and distances (ca. 17km for the "small cycle", 28km for the "grand cycle"), that's actually a perfectly workable alternative, if you like to be physically active.
The midday heat will be brutal though.
We have our own motorbike from Vietnam. No problems taking it into the Angkor Archeological Park. There are so many cars, tuk tuks, buses, motorbikes on site they would have a hard time only allowing registered vehicles, if that is even the case. As long as you have tickets for the park. We parked our bike in busy places like near food vendors.