Question: Is it possible for TeamCity to integrate to JIRA like how Bamboo integrates to JIRA? I couldnt find any documentation on JetBrains website that talks about issue-tracker integration.

FYI: I heard that TeamCity is coming out with their own tracker called Charisma. Is that true?

Answer: 
There is this plugin
<https://marketplace.atlassian.com/plugins/com.stiltsoft.jira.teamcity>
TeamCity has 3 build in Issue Tracking Systems:

1.BugZilla
2.JIRA
3.YouTrack

And there's a way to install the custom plugin for other ITS.
I did an integration with FogBugz issue tracking system with TeamCity 9.x.
<https://github.com/jozefizso/teamcity-fogbugz>