Can you hunt squirrels with 22 shorts?

I know this may sound like a dumb thing to ask, but I'm not familiar with the rifle. My dad pasted away several years ago, and he left me this rifle. It's really a nice one, but it's about 70 years old and I don't want to leave it in my gun case to go to waste. So is there something I can do with it, except target practice? Thank you.

REGULATIONS
Season Limit - 10
Arms & Ammunition: 1) Manually operated and semi-automatic 10-gauge or less shotguns with a capacity of no more than 3 shells in the
chamber and magazine combined; 2) Manually operated rifles and handguns .23 and less calibers; 3) Muzzleloading rifles and handguns 40
caliber or less and shotguns 10-gauge or less; and 4) long, recurve, compound bows and arrows, and crossbows. Single-projectile ammunition,
or fine shot pellets no larger than No. 4 lead, bismuth-tin, or tungsten-iron, or other approved non-toxic shot or No. 2 steel. Note: Rifle and
handgun caliber restrictions do not apply when hunting woodchucks or porcupines, although rifles and handguns must be manually operated.
Fluorescent Orange Requirements: Small game and porcupine hunters must wear at least 250 square inches of fluorescent orange at all
times on the head, chest and back combined. Woodchuck hunters must wear a solid fluorescent orange cap on the head. Orange must be
visible 360 degrees.
Hunting Parties: It is unlawful to hunt small game in a party of more than 6 persons. This does not apply to waterfowl or dove hunters when
hunting from a blind or other stationary positions.
Transporting Small Game: Small game may be transported untagged by the owner. Small game unaccompanied by the owner must be labeled
with the name, address, license customer ID number and signature of the owner.
No Open Season: Hungarian partridges, otters, pine martens and sharp-tailed grouse.
No Closed Season: English sparrows and European starlings. These species cannot be hunted during the regular firearms antlered and antler-
less deer seasons. No limit.

i didnt know it was a daisy red ryder bb gun lever action carbine with a compass on the stock and a thing that tells time..... ya you'll shoot your eye out kid.