Born in England, Kwesi spent his formative years at Kent-based Ebbsfleet United FC. He signed his first professional contract with League One side Peterborough United in 2008. Over the next few years, he was loaned out to several clubs playing in the Conference (aka the National League) – the fifth tier of English football and below.
After leaving Peterborough United, Appiah played non-league football in England briefly and in 2012, he signed a contract with Crystal Palace. He went out on loan from The Eagles to a number of sides in the lower tiers of English football – Cambridge United, Notts County, AFC Wimbledon and Reading FC are some of those clubs.
When his contract with Crystal Palace ended, the striker moved to English Football League One side AFC Wimbledon on a free transfer in 2017. The club did not renew his contract after it expired in June 2020 and the 30-year-old has joined ISL side Northeast United FC for the 2020-21 season.
In his last three seasons with AFC Wimbledon, Kwesi has scored 11 goals in 55 appearances in League One. Although he was with Crystal Palace for a number of years, he never played in the English Premier League for them. Appiah made his debut for the Black Stars in 2015 and he featured for them in the Africa Cup of Nations held that year – he has been capped six times for the Ghanaian National Team – the last one coming in 2019 against Mauritania.