Rental Companies Say No to Snow Chains
Sampling information from 3 car rental companies currently serving SFO would point to the harsh reality that car rentals generally don't include snow-chains in their list of additional options. What you get instead are snow/winter tyres, depending on rental season, availability and a bunch of other factors: the trick here is to call ahead and reserve. Quoting from the Avis FAQ (select USA → Equipment, Options and Special Requirements → Optional Equipment):
Ski Racks and Snow Tires
Avis offers ski racks and snow tires on selected vehicles in some U.S. locations. Please call ahead and check with the rental location after reserving online, or call 800-633-3469.
The Budget FAQ page on snow says that they don't offer show chains for rent, since these might damage the car:
What's the cost of snow chains?
Answer: Snow chains are not offered or available as optional equipment because of the potential damage to the rental vehicle. Many local restrictions also prohibit the use of snow chains.
The Enterprise FAQ page on snow goes even further by saying that it is forbidden to mount snow-chains on their rental cars:
Can I add snow chains? Can I be guaranteed a four wheel drive SUV?
Enterprise does not offer snow chains as additional equipment nor can snow chains be placed on rental vehicles. Our vehicles are equipped with all weather tires.
A specific vehicle option such as four wheel drive cannot be guaranteed. Please check with the branch upon arrival for availability.
Get Your Own Chains
Your best bet would be to purchase chains on your way to Yosemite. Supermarkets (Walmarts, etc.) and gas stations should stock them. Don't wait to reach the park to get them, since you're not guaranteed to find any, and once you do it might be too late. The Yosemite Park webpage on Tyre Chains says:
You can purchase chains or cables at most auto parts stores and gas stations, particularly in communities surrounding Yosemite National Park. A limited selection of chains is available for purchase at the Village Garage in Yosemite Valley and the Wawona gas station. Be sure to purchase chains or cables that match your tire size.
It's difficult to find businesses that rent chains; they're usually only available for purchase.
Rental car companies generally don't provide chains, however rental cars are not exempt from chain requirements, even if they have all-season tires.
Chains provide better traction than cables, however cables are easier to install; both are acceptable under the law. Your vehicle's owner's manual may specify that you use cables, not chains.
You could also try to buy/bring your own chains. You can find some on Amazon, with prices oscillating between 40-90
USD. The advice here is to avoid renting from companies whose rental contracts explicitly forbid you to mount them on the car (see Enterprise above), so to avoid incurring in extra damage fees. Also, do not show these to the rental company employees: last thing you want is for them to have an excuse to charge you for damage based on the fact that you are planning to mount chains on tyres. To bring your own chains you'll obviously need to know the tyre size in advance. This can be difficult since you are never guaranteed to get the car you reserve. Rather you are usually given a car in the same "class". A chain size smaller or larger than your tyre will obviously be useless.