Born in Gliwice, Silesian Voivodeship,[2] Cywka was part of the winning U-19 Gwarek Zabrze team which captured the 2006 Polish U-19 Championship.

Following a successful week-long trial at Wigan Athletic, Cywka signed a three-year contract in July 2006 transferring him from Gwarek Zabrze to the Premier League side.

In April, Derby manager Nigel Clough began talks to extend his stay at Pride Park Stadium into next season.

[6][7] On 25 May, it was announced that he would sign a two-year contract with Derby on a free transfer on 1 July, after turning down Wigan's extension offer due to his desire for first team football.

[10] He quickly returned to action, however, and grabbed this 2nd and 3rd senior goals with a brace in a 4–1 win over Watford on 30 October 2010, which earned him a place in the Championship Team of the Week.

[11] Cywka again started against Portsmouth at Pride Park and won a penalty after being fouled in the box, Robbie Savage scored the opener from the spot and the Rams went on to record a 2–0 victory.

[13] Despite the criticisms after the Portsmouth game Cywka made a further six appearances for the Rams before being ruled out for the remainder of the season with a knee ligament injury.

His first league appearance came in the seventh fixture, away at Nottingham Forest, but he was withdrawn after just four minutes when the dismissal of Frank Fielding led to the need for a tactical reshuffle.

Three late substitute appearances followed before he earned his second start of the campaign in the twelfth match of the season, away to Reading, when injuries had left Derby with just Cywka and Theo Robinson to choose from amongst the club's strikers.

[25] After leaving Chrobry at the end of his contract, he joined Lech Poznań's reserve team on 27 June 2022, signing a one-year deal.