Yes! In his death Jesus died for all humanity: he took upon himself all our sins and was punished for them. As a result we can be forgiven by God and made right with him (become “righteous"). Peter, who was one of Jesus’ disciples, writes this in his letter (1 Peter 2:24):

He himself bore our sins in his body on the tree, so that we might die to sin and live for righteousness; by his wounds you have been healed.

Jesus died to pay for your sin and mine. And he rose again to show that he has done it! He is now able to fulfill his promise of forgiving and saving all who come to him.

This offer of forgiveness and salvation is yours when you put your trust in him, when you acknowledge your sin before him and ask him to forgive you. It is as simple as that!! In his letter to the church in Rome (Romans 10:9), Pauls talks about it like this:

If you confess with your mouth , “Jesus is Lord”, and believe in your heart that God raised him from the dead, you will be saved.

There is nothing more that you have to do: all you have to do is want to turn back to God and live for him instead of yourself.