An American soldier stationed at a military base at Reykjavik, Iceland (UN forces?) somehow gets transported back to early settlement times.
He is taken in by a local Norse family and, realising he's stuck there for life, takes up with (and marries?) a local woman.
Then, for some reason he gets into a fight with a man from another family and, perhaps accidentally or perhaps because of his military skills, the other man is killed.
The MC does as he would have back in the USA and takes off. The dead man's family track him down. When they catch up with him he learns the irony of his actions.
By Icelandic law of the time, if he had owned up when the man died and taken the consequences he would have simply had to pay the family blood-money.
However, because he ran, he was as good as saying the death was murder and dishonourable so now the family would have to kill him.
Although I realise it's not very sci-fi apart from the time travel setup, I'm pretty sure I read this in a sci-fi anthology 1970s-1980s.