Yes, in a sense. It technically isn't vibrating them, but rapidly spinning them due to the constantly changing magnetic field (produced by the magnetron).

Since water has a dipole moment (one side of the molecule experiences a slight positive charge, while one side experiences a slight negative charge) it will react to changes in an electric field just like a magnet would

Edit: I'd also like to add this is not specific to water. Some fats and other food material also undergoes that rotation, and the same concept (with different frequencies and wavelengths) is used in industrial processes all the time to quickly, and efficiently heat materials