Parker came on as a substitute during the Glamour Boys' penalty-shootout defeat to Orlando Pirates in the Carling Black Label Cup on Saturday.
The former FC Twente forward revealed his delight to be playing for Chiefs and cited more exposure for the national team as one of the reasons why it was an easy decision to join the club.
"Joining Chiefs is a dream come true for me," he told the Sowetan. "I come from a family that is in love with Chiefs, so I also supported Chiefs from childhood.
"When Chiefs approached me, I had options to join clubs in Europe, in Greece and Sweden. I opted for Chiefs because the standard of the PSL has improved tremendously.
"I thought it better to come back home so I could be closer for the national coach (Pitso Mosimane) to see me on a regular basis.
"Bafana Bafana are on the verge of qualifying for the 2012 Africa Cup of Nations finals, I want to be part of that squad.
"I'm happy to have featured in the Soweto derby. It is the dream of any soccer player to be part of the derby, which is one of the biggest in the world.
"I came here knowing very well that there is so much pressure but I'm here to contribute to the success of the club. I want to win trophies with Chiefs.
"I was very happy with the manner in which I was welcomed at Chiefs. I also met the club boss, Kaizer Motaung, who told me that he is glad that I had finally joined the club."