Norshie started her career with Valued Girls when she was part of the Ghana U17 squad between 2015 and 2019. In February 2019, Norshie and two other players from Valued Girls were signed by Nigerian club
Edo Queens on a six months loan deal. She later left the club permanently and joined
Ghana Women's Premier League side
Berry Ladies in 2020. On 18 January 2021, she made her debut in a 3–2 victory against Immigration Ladies. She started, played the full 90 minutes and scored her debut goal which was the first goal of the
2020–21 Ghana Women's Premier League season. In May 2022, Norshie joined the KC Courage of the United Women's Soccer League. She started and played the full 90 minutes of the entire 2022 season. She was named to the United Women's Soccer All-Central Conference First Team and Iron Woman of the year (most minutes played). == International career ==