There are multiple ways to open links in Tweets to view them in the browser. You can long press a Tweet to open a pop-up menu which displays and allows you to open any of the links in the Tweet, including web links, @usernames, image links, & hashtags. You can also access this menu by tapping the Tweet to open the Tweet action menu and select the ‘Links’ option from the menu.
If you would prefer that links not open in an external browser window, you can enable the Integrated Browser setting to use an in-app browser for faster browsing. You can find this setting in the General section of the app settings.