'and He reckoneth it to him -- righteousness.'
It's easier to understand the meaning of 'reckoneth' when you look at the entire sentence.
The sentence is saying, 'God thought of him or considered him as righteous' (because of his faith).
So a close 'direct' translation of 'reckoneth' is 'gave' or 'assigned' or 'considered'. But, it is far better to translate the entire sentence (because it is old English) to obtain the entire meaning.
"And he hath believed in Jehovah, and He reckoneth it to him -- righteousness" = 'The person who believes in GOD, God considers that person righteous.'