Oh, I see what you mean now.
Yes, that is possible using oAuth Access. Please check out this article: https://confluence.atlassian.com/display/JIRACLOUD/Allowing+OAuth+Access
Let us know if this helps you.
The only external service we allow customers to use on JIRA Cloud to authenticate is Google Apps.
If you'd like more info about it, please refer to: Setup Google Apps for your site.
On Bitbucket you can use: Google Apps, Facebook, Twitter, and Github accounts.
Let us know if you have further questions.
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