Yes, Cats CAN Get Heartworms
Spread by infected mosquitoes, heartworm is increasingly being recognized as an underlying cause of health problems in domestic cats. Despite its name, heartworm primarily causes lung disease in cats. It is an important concern for any cat owner living in areas densely populated by mosquitoes, and prevention methods should be discussed with a veterinarian.
ASPCA heartworm information.
VCA Animal Hospitals heartworm signs and treatment.
American Heartworm Society