Per Sony's specification page, your laptop has an i3-2310M. This CPU
is modular, so you can technically remove it and replace it. Will a compatible upgrade work? That very much depends on the computer's BIOS.
For reference, here is a list of mobile CPUs that are the same generation and use the same socket as your current CPU:
https/ark.intel.com/products/codename/29900/Sandy-Bridge#@mobile
Unless Sony Support or some other source can confirm an upgraded CPU will work, this will be a matter of trial and error.