This righteousness that Paul is speaking here is that which is of the obedience of faith that verse 5 speaks if we hold to the context of the passage..
(Net
Rom 1:5) Through Him we have received grace and our apostleship to bring about the obedience of faith among all the Gentiles on behalf of his name.
As he continues to verse 17 he says in 15 that he is ready to preach the Gospel and that he is not ashamed of it, for in it is the power of God unto salvation. Because there in the righteousness of God is revealed from faith to faith. For the just, the lawful out of faith shall live. Because that which may be known of God is manifested in them. For the invisible things from the creation of the world are clearly seen, so they are without excuse. For God has said, I will put the word in their mouth and in their hearts, that is the word of faith in which we preach. "For with the heart man believeth unto (INTO in the Greek) righteousness"
Rom 1:15 So, as much as in me is, I am ready to preach the gospel to you that are at Rome also.
Rom 1:16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.
Rom 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
Rom 1:18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness;
Rom 1:19 Because that which may be known of God is manifest in them; for God hath shewed [it] unto them.
Rom 1:20 For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse:
Rom 10:8 But what saith it? The word is nigh thee, [even] in thy mouth, and in thy heart: that is, the word of faith, which we preach;
