Cats can drink small amounts of chicken soup, but it's recommended to skim off the surface oil before giving it to them. Excessive oil can cause diarrhea and put a strain on their pancreas and liver. Do not add seasonings to the chicken soup, as too much salt can affect a cat's kidney metabolism. Finally, be sure to remove any chicken bone fragments from the soup. 
Benefits of chicken soup for cats.
Chicken soup is warming and nourishing, so it's fine for cats with colds to drink it to replenish their nutrition. If a cat has a mild cold, it can recover on its own by taking appropriate measures to keep it warm. However, if it's a more severe cold, with symptoms like coughing, runny nose, sneezing, fatigue, and loss of appetite, then some treatment measures should be taken.