There are plenty of tools for online browser testing like LambdaTest, Cross Browser Testing, Browserstack, Saucelabs, etc.
You can read the review for which tool to use:
Depending upon your needs for cross-browser testing you can choose the best tool for you.
I will recommend LambdaTest (Disclaimer: I work for LambdaTest) as it provides you with a cloud of more than 2000 combinations of browsers, browser versions. operating systems, devices, and resolutions. It is one such tool having integrations with many of the bug management and communication tools like JIRA, Asana, Slack, Trello, Github, Gitlab, Bitbucket, VSTS, and a lot more coming. It has 24*7 customer support and many features to ease your browser testing like Wordpress plugin, Chrome Extension, and a lot more.