Engin Baytar was born and raised in Germany to Turkish parents. He first joined FC Gütersloh before transferring to Arminia Bielefeld in 2000. Engin Baytar spent four years with the club's reserve team before moving to Turkey-based club Maltepespor in 2004. He spent two at the club before moving to Gençlerbirliği, who loaned him out to Eskişehirspor for the second half of the 2008–2009 season. Engin Baytar wears the number 50 on his jersey because he is from the Central Anatolian Province of Nevsehir in Turkey. His father is from Trabzon and mother is from Nevsehir.
On 17 August 2011, Engin Baytar joined Galatasaray for 2 years for a fee of €1.1 million. He made his first assist at the match against Bursaspor to Johan Elmander on 26 November. He scored his first goal with Galatasaray against Sivasspor. But unfortunately he also got a redcard in the same game. He returned to the club after a loan-spell for the new season, but haven't still found himself a place in the first-18 for fortunate reasons.