Rajczi started to play football in Kaposvár, playing for Kaposvári Rákóczi FC. He played many seasons with Rákóczi, and scored a number of goals, reaching the topscorer title once in the second division. In 2003 he was signed by Újpest FC, where he became one of the most respected Hungarian strikers. Rajczi won two silver medals in the championship with Újpest.
Péter Rajczi became the topscorer of the Hungarian league in the 2005/06 season by scoring 23 goals in 24 games.
He joined Barnsley F.C. on 29 January 2007, for a substantial loan amount, and has the option to sign permanently in the summer.
He was a used substitute in Barnsley's game with Cardiff City F.C. on Fri 2 February 2007. Peter scored his only Barnsley F.C. goal against Hull City on 20 February 2007.
At the end of the 2006/2007 season Rajczi returned from loan to Hungary and joined Újpest FC again.
After a season spent at Pisa Calcio in the Italian Serie B, he currently plays for Újpest FC.