Check out this helpful article from the Animal Humane Society about how to introduce your cat to a new pet.
How to introduce a dog and cat
Despite the stereotype, many dogs and cats learn to live together peacefully. Be patient and take the introduction process slowly, but know that whether or not your pets get along will also depend on their individual personalities. Follow these steps to maximize the chances of success.
Keep the pets separate at first
Keep the pets separate for at least the first 3-4 days. Prevent any contact until your new pet has had his vet checkup and been cleared of illness. Confine your new pet in a sanctuary room with the door closed or a separate floor of your house. The goal is to allow the pets to get used to each other’s presence without face-to-face contact. Even if they can’t see each other, they can hear and smell each other.
Feed them on opposite sides of a closed door
The idea is to teach them to associate the presence of the other pet with pleasant things, such as food. With each feeding, move their food bowls a little closer to the closed door. Continue this process until each pet can eat calmly right next to the door.
Teach basic commands
If your new pet is a dog, start teaching him basic obedience cues, such as “sit” and “down.” Keep training sessions short, pleasant, and rewarding for the dog. Learn more about training with Animal Humane Society's Training School.
Begin face-to-face meetings
Once your pets can eat their food calmly right next to the door, conduct meet and greets in a common area of the house. Don't use either animal's sanctuary area. Keep the first few sessions short and calm. Keep the dog on a leash and let the cat come and go as he wishes. Do not restrain either pet in your arms, as injury could result if either pet behaves aggressively. Ask the dog to sit and reward him with small tasty treats for calm behavior. Give your cat treats as well. If either pet demonstrates aggression, calmly distract and redirect them. Toss a toy for the cat to lure him from the room, or call the dog’s name and reward his attention. Return the pets to their confinement areas.
Repeat sessions daily
Repeat these face-to-face sessions daily. Save your pets’ favorite treats for when they are together. If the cat attempts to leave the room, allow him to do so, and do not let the dog chase him. Try to end each session before either pet shows stress or aggression.
Allow pets loose together
When the animals appear to be getting along well, allow them loose in the room together, keeping the dog’s leash attached and dragging on the floor so that you can step on it and prevent him from chasing the cat if he gets excited. If tension erupts, go back to the earlier introduction steps and repeat the process. Make sure the cat has access to a dog-proof sanctuary room at all times.
Proceed with caution
Continue to separate the pets when you are not there to supervise.