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.