Can a liquid turn to a solid by applying pressure?
It is possible to change a liquid into a solid, or in general change the phase a substance finds itself in by just altering the pressure.

You might want to refer to some graphs known as Phase diagrams that portray the effect of temperature and pressure on the physical state of a substance.


(source: purdue.edu)    

In this example if you're to draw a straight line from the point B to D, it'll have a subtle positive slope. So there's a possibility to transform a liquid into a solid without making any changes to the temperature conditions.

You might have heard of solid $\ce{CO2}$ or dry ice. I might be wrong but a part of me says carbon dioxide is pressurised and refrigerated for it to form.

An interesting thing to note here is that in case of a gas turning into a liquid, there's a temperature known as Critical Temperature ($T_c$) above which the gas cannot be liquified no matter how much pressure is applied.