The 21-year-old is a former Everton Ladies and Durham Women stopper.
"It's a dream to have signed for Arsenal Ladies," she told the club website.
Manager Pedro Martinez Losa added: "Anna is a powerful, towering keeper who is very driven and eager to develop. I'm looking forward to working with her."
Women's Super League One club Arsenal Ladies have signed Doncaster Rovers Belles goalkeeper Anna Moorhouse.