Abraham is Paul's first example. Paul knows that if he can make a convincing case for Abraham's justification by faith, Jews might be more open to considering the claims of the gospel. After all, if the ancestral father of the Jewish nation did not attempt to earn his way into God's favor, neither should his offspring. Paul was anxious that his fellow Jews discover what he and their father Abraham had discovered- that justification comes by faith (Life Application Commentary: Romans, 81).
And secondly, the Hebrew text of Genesis 15:6 as it stands is ambiguous, having the possiblity of meaning “and he (Abraham) reckoned it (God’s promise) to him (God) as the right thing (i.e., true).” This would be saying the same thing as the immediately preceding statement (“And Abraham believed God”) in slightly different words, a kind of poetic parallelismus membrorum. But the translators of the Septuagint (and undoubtedly Paul also) wished to exclude that possible alternative interpretation, which they considered wrong. So they changed “he reckoned it” to “it was reckoned,” which makes the alternative interpretation no longer possible.