Did Juliette Gordon Low speak American Sign language?

No, Juliette Gordon Low was not known to have ever learned or spoken sign language.

Due to the fact that she was not completely deaf and that her hearing loss occurred later in life, Juliette probably did not learn sign language. In fact, there are stories about how she used her hearing loss to get people to do things she asked them to do. If they tried to tell her "no" she would just go on talking as if she had not heard them.

Also keep in mind that there was a lot of stigma about sign languages prior to the 1960s.