No, you can't. There are three types of cold virus to infect people, rhinovirus, coronavirus and respiratory syncytial virus, and these three viruses are split into approximately 200 "subtypes". They are responsible for a range of symptoms including sneezing, sore throat, runny nose, and fever.
Cats too get colds (well, technically they get the flu), but with different viruses. Herpesvirus and calicivirus are the main offenders. Symptoms are similar to colds in humans with runny noses, sneezing, fever and eye discharge.
Viruses are funny little things, they are essentially a piece of DNA or RNA surrounded by a protein "coat". They replicate by entering specific cells in their host and using the host's cellular machinery to replicate. In order to enter the cell, the virus attaches to it, and receptors on the viral coat attach to complementary receptors on the cell wall, gaining entry. I look on this as the virus having the right key to unlock the cell door. If the virus doesn't have the right receptors (key), then it will not be able to enter the cell.
For this reason, many viruses are animal and even cell specific because they only have the key to that animal/cell. For example, the herpes virus is found in many species of animal, but it is generally host specific. We can't catch feline herpes, cats can't catch human herpes. This is the same with colds. The viruses responsible for cat colds can not gain entry into our cells, and therefore we can not become infected.
There are some viruses which are "zoonotic", which means they can be transmitted from other animals to humans and vice-versa. Rabies is a life-threatening virus which is found in many mammals including cats and humans.
People get colds from other people. The virus is spread via airborne viral particles which are released when an infected person coughs and sneezes and/or via fomites, inanimate objects that are infected with the virus (such as telephones, door handles etc). Cats get colds in much the same way. This is why it is so important to regularly wash your hands as well as keep your fingers out of your mouth, particularly if somebody around you is infected.
So to summarise, if your cat has a cold, there is no need for you to worry, you can not become infected, nor can a cat catch a human cold. Proper hygiene must be practiced around a sick kitty, though, to help reduce the chances of spreading the virus on to other cats.