Local media had called on Capello to take away the armband after Arshavin was heavily criticised for his performances during Euro 2012.
The Italian, who replaced Dutchman Dick Advocaat as coach last month, said on Tuesday he was ready to give the 31-year-old another go.
"Everyone deserves a second chance," former England manager Capello told reporters at the team's training base near Moscow.
"This is his chance to prove to everyone that he still plays an important role in this team. I want to see Arshavin showing his best quality on the pitch and again becoming the player everyone loved to watch."
In February, Arshavin rejoined former club Zenit St Petersburg on loan from Arsenal following a turbulent year at the London club but failed to rediscover his best form.
He was also seen as one of the main culprits for Russia's Euro 2012 flop, with the slightly-built striker forced to issue an apology to fans after the team failed to advance past the group stages in Poland and Ukraine.
"Arshavin doesn't deserve to be Russia captain, he just doesn't have the proper qualities and the ability to lead the team," former Soviet international Yevgeny Lovchev, now a leading columnist, wrote in the daily Sovietsky Sport last month.
The player's club future has also been in limbo, with media reports saying he is likely to leave Arsenal before the transfer window closes at the end of the month.