Can this processor run Skyrim?

In all honesty, I doubt it. To be honest, I can't tell you for sure because I haven't done it myself and I don't own skyrim. If someone does own skyrim and is willing to disable all other cores in their system, they might be able to tell you, but even still if they get it to work it is no guarantee because the different architecture and clock speeds of a newer chip.

My suggestion is to save your money and upgrade because even if it does run, it probably won't run well.

What gpu do you have?

im thinking you need a dual core atleast

Don has done some of the hard work for you so check out his article below:

http://www.tomshardware.com/reviews/skyrim-performance-benchmark,3074-9.html

Some games don't even start with a single core cpu

I am running skyrim with a single core (AMD Athlon 64 FX-55) and a Radeon HD 4650 GPU with 3 GB of RAM and I am getting around 30-40 fps with low shadows and high-ultra everything else and 4x AA, though the controls are lagging behind around 5-10 seconds when there is a lot on going on in the screen (2-3 bandits) and load times are a little slow. I have to set skyrim to a high priority every time I start the game as well. I think the game is fine but it is frustrating hitting the attack button and 5 seconds later spraying fire non stop all over the place, wasteing my magicka.

I think it is because the processor cant process my mouse and keyboard input at the same time as Skyrim, but I haven't found anything from a google search on it yet.

Edit: I turned off AA AF, and went in windowed mode and now I have a decent fps AND no delay with my controls, so I am happily playing Skyrim on the PC now!