About the only animals Animal Care & Control (ACC) accepts without question are "owner-surrendered" pets or those brought in by their own Animal Control Officers.

If you find a dog wandering the streets, before bringing her to ACC, exhaust all methods for finding her guardian yourself: Check for guardian contact info on the dog, file a found dog report with ACC by phone, post descriptions on social media and lost dog sites — do anything, as the shelter's website says, "to best help" ACC:

https://www.sfanimalcare.org/lost-found-pets/report-a-found-pet