That depends on how technical you get with the definition of “singing.” It can just refer to making or performing musical sounds. Cats do that all of the time, when they meow or even howl in a melodic way, but scientists don’t usually refer to these behaviors as singing.
Bats, rodents, whales, some fish, grasshoppers, and humans — as well as other animals — are known to have their own songs. For example, Kirsten Bohn, Mike Smotherman and their colleagues in the Texas A&M Department of Biology determined that certain male bats have very distinguishable syllables and phrases that they use as songs to attract females, and in some cases, to warn other males to stay away. Says Bohn: “We’ve learned the vocal production of bats is very specific and patterned.” That’s important, because it puts bats on a short list with whales, birds, humans and a handful of other animals that create specific, repeatable songs.
Cats are not usually mentioned on such lists, probably because their communications rely so strongly on other non-audible factors, such as body language, touch and scent. They do, however, possess an “extensive vocal repertory,” according to Jacque Lynn Schultz, companion animal programs adviser for ASPCA National Shelter Outreach. This wide range of cat sounds — permitting cats to express their emotional state — includes meowing, caterwauling (such as before fights), chattering, growling, purring and, last but not least, screaming.