Is there a way to automatically map requirements to a test case when importing test cases?

You are correct in your description of what's possible: it's a manual process.  To help with that process...

• When you import your test cases you could add a label to each test case that maps to its related requirement
• Then use a Filter on the Test Case screen to find and select all test cases with 'x' label
• Then use the More>Bulk Edit feature and select the "Coverage (issues)" option to link all selected Test Cases to the relevant Requirement (issue)
• And optionally, delete all labels using the Configuration menu