Jones required surgery on the injury over the summer and had been a doubt for his country's Six Nations opener against England on February 6.
But the 28-year-old tight-head is now back playing for his regional side the Ospreys and is hoping to perform well enough over the coming weeks to secure the Welsh No3 shirt next month.
"The shoulder is okay now and it's nice to be back," said Jones, who featured in the first two Lions internationals in Durban and Pretoria.
"I want to get some form over the next few weeks and my target is to get some starts. I don't think it will take me too many games to get back up to speed.
"Then I hope to get picked for the Six Nations and England first up. But that is down to Mr Gatland."
Jones enhanced his reputation significantly during the Lions' 10-match tour of South Africa, solidifying the tourists' scrum during the second half of the opening rubber and the first half of the second.
And the double Grand Slam winner has no doubt that his performances for Britain and Ireland's elite were a career highlight.
Now his focus is on regaining that form for club and country as quickly as possible.
"I need to work hard and get back to the level where I was at before and on the Lions tour," added Jones.
"It was the best rugby of my career. It was a brilliant tour and I really enjoyed it. There had been a lot of negativity from the 2005 tour but the team spirit was exceptional.
"But that has gone now and I need to get back into the swing of things. The game has changed so much in the six months I was out.
"I've always been confident in my own ability but it's nice to hear praise from people. But with that comes a lot of pressure."