Immunity from having the disease does not count.

All restaurants, bars, clubs, gyms and larger indoor venues will be required to obtain proof of vaccination from patrons and employees to protect against the continued spread of Covid-19.

Here is the official declaration:  “We know that for our city to bounce back from the pandemic and thrive, we need to use the best method we have to fight COVID-19 and that’s vaccines,” said Mayor Breed. “Many San Francisco businesses are already leading the way by requiring proof of vaccination for their customers because they care about the health of their employees, their customers, and this city. This order builds on their leadership and will help us weather the challenges ahead and keep our businesses open. Vaccines are our way out of the pandemic, and our way back to a life where we can be together safely.”  

It seems that you need only show your CDC Vaccination card to enter.

Hope this helps! Dean and Andie