Yes you can waterproof a non waterproof jacket.
To make a non waterproof jacket waterproof you can buy some water repellent spray and spray the fabric water repellent onto the jacket.
The water repellent spray will help the water shed off the jacket more easily.
Although the jacket won't be entirely waterproof the water will not stay on the jacket as much as it did before.
I've used some water repellent spray on my jacket and it does help to keep the water off the jacket so it doesn't get drenched with the water.
It makes drying the jacket much easier as well because most of the water ran off the jacket.