Can I use a stove as a deep fryer?

as long as you are careful

Yes, it can be safe, I do that all the time.

Go out and buy a thick sided pan, straight sided if you can find one.One that stays setting firmly on the burner even if there is nothing in the pan. Buy an appropriate fire extinguisher. Have a tight lid for you pan, to cover a fire if one should occur. And keep all flammable materials away from the stove. 

Buy a sturdy candy thermometer that clamps onto the side of the pan. 

Be prepared to watch the pan the entire time the heat is on. Do not even look away. And never ever fill the pan more than half full with oil, it must have room to bubble. 

I add just enough oil to the pan, French fries are easy, I do not cover them with the oil, just almost cover them. They get done without turning them. 

Most things I do the same way, fry it on one side, and turn it over to make sure it gets brown both sides. 

Do you mean heat the oil on your stove top? You can, but be damn careful. Make sure you have a frying thermometer and make sure you understand all the precautions you need to have in place to deep fry on a stove top including a kitchen fire extinguisher. 

no go to store and buy one

I always did deep frying on the stove top in an iron skillet with about half an inch of fat and I turned over the pieces of say catfish steaked out getting them golden brown on one side then turning them. Chicken wings  would oiften get done without turning them. But for years I never owned or used a deep fryer. Now for health reasons I use an air fryer. Picture shows wings and fries done with air fryer

If you follow Food Network, some of their chefs use a heavy enameled cast iron duch oven on the stovetop with vegetable oil about 2/3 of the way to the top and a deep fat/candy thermometer.

No.  It is impossible to use a stove as a deep fryer.  There is no way to fill a stove with hot oil.

This is a small stove.  Notice, totally impossible to fill with oil.

Yes.  But you need a fairly heavy duty pot with high walls.  It's not recommended as pots can easily get knocked over and hot oil is very dangerous.  Dedicated deep fryers are designed to be stable on the counter and not tip over  

LOVE to see you try. 

No.  But you can use the stove's heating element to heat oil contained in another vessel.