No. This is a very common belief because they share the same name, but this is not true. Dietary fat that you eat in your food is essential for your body in certain amounts. Adipose tissue, or body fat, is simply stored calories. While eating foods high in fat can result in excess adipose tissue, consuming dietary fat in the correct amounts will not make you fat.
Dietary fat is simply another form of energy and nutrition; it does not directly correlate at all to actual body fat. The right fats supply the body with energy, help it retain crucial vitamins that require fat for absorption, protect the organs, and encourage healthy skin and hair.