No. You can't.
As S.C.Madsen and int3 already posted, you can declare static const in class scope for any type, as long as it is properly defined (in the cpp file) and initialized, But it can't be a compile time constant.
Compile time constant is a constant you can use as template argument and as built in arrays' size. These constants may also be optimized better than run-time constants. Currently, AFAIK, only the built in numeric types may serve as compile time constants.
The reason, BTW, is that this constant should be evaluated at compile time (similarly to literals).