I just attempted this in Sitecore 8.2 Update 5 with no issues. Here are the steps.
Open an Item with a Rich Text field and enter some text.
Select the text you want to use for your anchor tag and then click the Hyperlink Manager button. You should be presented with the pictured dialog. Note that to set an anchor, you need to switch to the Anchor tab in the dialog.
Select the text you want to use to link to your anchor tag and click the Hyperlink Manager button. You should be presented with the pictured dialog. Note that the Anchor field will allow you to pick from anchors that are already inserted into this particular Rich Text field. Upon selecting the anchor, the URL field should automatically update to the identifier for the selected anchor, with no protocol, hostname, or path, as expected.
At this point if you accept out of the Rich Text Editor and save your content, your anchor and link should be all wired up. Here is the HTML from my example to show what markup is produced in the background: