I have a nice birdbath but there is a small hairline crack in the
birdbath dish, probably occurred during a move. Is there something I can
use to seal the crack?

Silicone caulk will work, but water will again begin to leak around the
patch, unless you trowel it on with a putty knife, sorta like paint.. I've
used a waterproofing paint, starts with the letter "U". Quikcrete also makes
a waterproofing paint especially for cement products - I think it is called
quikcoat. Also, check for toxic additives, since we are talking birds.