An electric potential is generated when a liquid moves with respect to a solid (streaming potential). Is the reverse true? Streaming potential is an electrochemical phenomenon that a that relates
electric currents with the relative movement of solid and liquid phases in contact with
each other.

So when a liquid moves past a solid a potential is generated. The equations for the values of the potential and current generated can be found in this Wikipedia article. My question is, is the reverse true? If I applied an electrical potential difference (instead of applying a pressure difference), would a pressure difference be generated?
Your assumption is correct. Electrokinetic pumps use a potential difference across an osmotic membrane, i.e. through narrow channels, the inverse of flow causing a streaming potential difference. There are other aspects of the phenomena such as electrophoresis, capillary osmosis etc.; see:

Electrokinetic Phenomena a

On the Efficiency of Electrokinetic Pumping...

and

short video demo