I don't know of any tool which selects based on the 3D cursor, however 3D view > Select > Select loop inner-region does pretty much does the equivalent.
It selects the side with the least geometry, so if that's not the side you want, invert the selection with CtrlI, or enable Select bigger in the redo panel immediately after running the operator (F6) or at the bottom of the tool shelf (T).
I think this tool was originally designed to select boundary loops which formed a ring like this, which might make the behavior of this tool appear more clear/intuitive:
Note that you can use select boundary loop to select the ring around the selection (the exact opposite behavior of select loop inner region). See the above gif.
There are only two possible selections based on such a boundary loop (one side or the other side), so IMO using the cursor is probably overkill.