Can a 2014 ford fiesta tow 1300 lbs.

No, too small of car. Only up to maybe 500 lbs.

A Fiesta only weighs about 2500 lbs, so even if it could pull it, stopping and control would be FAR past the limits of safety.

I Own A 2016 Chevy Sonic, That Is Not Rated For Towing! With The Dealers Help, A Towing Package, Including Coolers Were Installed! I Pull 4x10 Trailer, With A 4-Wheeler With Toung Jack And Spare Tire, Weighing 1100 Pounds! It Does A Fantastic Job! It's A 1.4 Turbo With 168 Tq And 158 Horse!

If you lookat the small plate on the tow bar , this will indicate the maximum power and the maximum Gross Vehicle Mass or trailer loaded weight you can legally tow with that vehicle.