The righteousness of God through trust in Jesus Christ is given to all those who trust Him (Romans 3:22).
God is just (righteous) & God is the justifier (the one who makes you righteous, the one who makes you right with God) of anyone who has trust in Jesus (Romans 3:25).
A man is justified (made right with God, made righteous) by trust apart from works of the Law (Romans 3:28).
I do not have a righteousness of my own derived from the Law. My righteousness comes through trust in Christ. Christ's righteousness comes to us from God on the basis of trust. (Philippians 3:9)
Other Meanings of Righteous are:
innocent, faultless, guiltless, approved of God, acceptable to God
David speaks of the blessing on the man to whom God credits righteousness apart from works: “Blessed are those whose lawless deeds have been forgiven, and whose sins have been covered. Blessed is the man whose sin the Lord will not take into account.” (Romans 4:6-8)
"Not take into account" can also mean "not count, not charge, not impute, not reckon."
"Blessed is the man who by no means the Lord will charge with sin." (Romans 4:8 WEB)
God counts us as righteous if we trust in Him, the One who raised Jesus our Lord from the dead. Jesus our Lord was handed over to die because of our sins, and He was raised from the dead to make us right with God, to make us righteous. (Romans 4:24-25)
Those who receive God's abundant provision of grace and of the gift of righteousness reign in life through the one man, Jesus Christ. (Romans 5:17)
All who receive God's wonderful abundance of grace and his gift of righteousness will live in triumph over sin and death through this one man, Jesus Christ. (Romans 5:17)