Yes but try public transport which is great, if a little expensive.
There Are definitely parking lots around these piers, but they are quite pricey. If you are lucky, try to find one of the street aide parkings further in from the piers, they are free but have time limits. So they are good for short stays. If you are going to take your time on Alcatraz, then park somewhere further away in SF, and Uber or Lyft in for best prices.
Yes, there is parking but it is really, really expensive. The best way is to use Uber or Lyft.
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