Can someone help with this? Its the first part I am unsure of- gecmisini siktim. Thanks in advance

gecmisini siktim sabahın köründe arıyorsun uykusuz kaldim

 geçmişini i think means your past

the other can be or "siktim" or sıktım"

It is rude.

literally something like "I f**k your history" but we can say "f**k you, you call me in the cockcrow (very early in the morning), I couldn´t get my sleep.

 This sentence seems weird. I think it must be like this: "Geçmişini siktiğim, sabahın köründe niye arıyorsun? Uykusuz kaldım."

We can translate it as something like that:

You whose past i fucked! Why do you call me in such an early time? You made me unable to sleep.

you cannot expect someone who says this to say it in a grammatically perfect way. can you?

sabahın köründe = at the crack of dawn