I am thinking that the electrostatic force (Van der Waals force) should take effect when I try to tape an ice, but the tape slips. Why does this happen?
In short, this is because the surface of an ice cube is wet, i.e, made of a liquid layer.
You can bind the scotch tape to its water molecules close by, but they will flow away from the rest of the liquid layer easily, preventing you from transmitting a pulling or shearing force between the scotch tape and the ice cube.
The reason for this liquid film is that ice's crystalline structure always has defects at the surface. Defects imply that the melting temperature is locally lower: the surface melts before the core. If you perform this experiment in a very cold ambient temperature, you may succeed in breaking this thin film and get adhesion (and you might even succeed binding the cube to your fingers).
Further reading: Why Is Ice Slippery?