Yes, I sing to my cats all the time. I usually just make up silly words to whatever's on the radio or comes to mind .... I know they think I'm nuts

One of my favorites is sung to the tune of Don Ho's "Tiny Bubbles"

Mitzi noodles, fluffy my babboo
Mitzi noodles, boy to I love you
Mitzi noodles, you are so CUTE
and I love my Mitzi noodles,
Ooh-Tee-Ute