Yes astigmatism can run in the family so if someone in your family such as a sister, brother or even the father or mother has astigmatism then it's possible that the baby can be born with astigmatism.
Astigmatism is able to be passed down through genes genetically but it's not contagious so you cannot catch astigmatism from someone in your family.
But you certainly can get astigmatism through the genes that are passed down through the blood in the pregnancy.
My nephew has astigmatism and was diagnosed with it at age 2 and his mother also had astigmatism when she was 2 years old as well and still has it.
So I would say that my nephew got the astigmatism passed down to him from his mother.