The 27-year-old registered 1:06.52 minutes in her semi-final, equalling the time of American swimmer Katie Meili.
China’s Jinglin Shi was second in 1:06.31.
The American swimmer Lilly King was first in 1:05.70.
The final will take place tonight at 8:44 pm – local time.
Atkinson has never won an Olympic medal but came close at the previous Olympic Games held in London four years ago with a fourth place finish.