This particular database isn't available on FamilySearch.com.
However, it appears that different databases are available at the Family History Libraries as microfilm that might cover the same region and overlapping dates, though I have no idea if they have the same/similar records.
The original data for this collection is listed as from: Zivilstandsregister, 1874–1945. Digital images. Landesarchiv, Berlin, Deutschland.
I like to search both Ancestry and FamilySearch and usually will put the citations for both on my profiles when I can find a record in both locations. I think that really helps folks that don't have an Ancestry account.