No, the color of the car is not generally one of the factors that an auto insurance company will use as a rating factor.
The myth is out there that a silver or red car costs more to insure but in all actuality insurance companies do not consider the color, but they do look at the type of car. If it is a red sports car it will likely cost more than a green family car to insure but because of the powerful engine and statistics of accidents relating to sports cars compare to a four door family sedan, not the color.
Some other factors that insurers consider include your age, the kind of vehicle you drive, your claims history, in some states your credit history and your driving record.
To get a quote for your red, silver, black, tan or any color in the spectrum follow this link from an auto insurance specialist.