No, cats have different nutritional needs to dogs. While dog food may look the same, it has ingredients tailored to that of a canine. Feeding a cat dog food can lead to nutritional deficiencies and possibly death.
Cats are obligate or true carnivores which means they require meat in order to survive. In the wild, their prey will consist of mostly protein, with a moderate level of fat and small amounts of carbohydrates. Dogs, on the other hand, are omnivores, which means they eat animals along with some plant material. Dog foods are often cereal based, and lacking the animal proteins that your cat requires.
Protein and amino acids:
Cats have a higher need for protein than dogs due to their metabolic requirements. Every cell in your cat's body contains protein, which performs a number of functions including growth and repair of tissue, used as a source of energy and regulating metabolism. Proteins are the major components of hair, skin, tendons, ligaments, cartilage and nails. Cats require approximately 23-26% of the protein in their diets compared to dogs who need between 18-22%. 
When protein is digested, amino acids are left. These are the building blocks of protein.
They fall into three groups:
- Essential amino acids - These are amino acids which can not be synthesised by the body, and therefore the cat needs to obtain them from the food they eat.
- Nonessential amino acids - Amino acids which can be produced by the body.
- Conditional amino acids - Nonessential acids which become essential amino acids at times when the cat's body is stressed or sick.
As dogs have different nutritional needs to cats, their diet lacks essential amino acids which are vital to the cat. The most notable ones being taurine and arginine.
Taurine is an essential amino acid which is found predominately in meat and seafood. Cats require taurine for normal heart function, neurological development, bile salt formation, reproduction, and vision. Felines can synthesise small amounts of taurine in the body, however, most is obtained via the diet (which is why it is known as an essential amino acid). Since the 1970's it has been added to all commercial cat food. Dogs are better able to synthesise taurine in the body, and therefore it is not necessary to add it to their food. Feeding a cat dog food will result in taurine deficiency.
Another essential amino acid, arginine is responsible for protein synthesis and ammonia detoxification. A diet lacking in arginine will result in a cat with hyperammonemia (excess of ammonia in the blood), resulting in vomiting, muscle spasms, unsteady gait, hyperesthesia, and spasms, eventually, death will occur.
Fats provide the cat with energy. They are necessary for the absorption of fat soluble vitamins and for the production of certain hormones.
Arachidonic acid is an essential omega-6 fatty acid Dogs are able to synthesize linoleic acid (found in many vegetable oils) into arachidonic acid, cats, however, are lacking the necessary enzyme to do this and cats must obtain this from their diet.
Unlike most mammals, cats are unable to convert vitamin A precursors (beta carotene) into active vitamin A (retinol). Dogs are able to convert carotenoids in plant matter into active vitamin A, however, the cat must consume all his vitamin A as free retinol from animal tissues. Vitamin A deficiency is rare in cats fed commercial cat food diets as adequate amounts are added.
Niacin (vitamin B):
Most other species of animal are able to synthesize niacin from the amino acid tryptophan, however, cats can not do this and must obtain this through their diet. Niacin is a water-soluble vitamin, meaning they are not stored in the body, and must be replaced continually. Niacin helps the body convert nutrients into energy, nervous system function, and for healthy skin, coat, liver and eyes. Niacin is found in plants but in much lower levels than in meat.
So as you can see, a cat's nutritional requirements are quite different to that of the dog. There are many nutrients which are essential for the cat to obtain via the diet that is either not found in dog food, or in levels that are too low to meet your cat's needs. Feeding a balanced diet specifically for cats is absolutely essential. Any commercial cat food should meet AAFCO standards.
 Canine and Feline Nutrition - Case Hirakawa and Carey Daristotle