Yes, YouTrack lets you import issues from other tracking systems with our REST API. We also provide a Python Client Library, that wraps the REST API and allows it to be used with Python scripts.
We've published a library that contains several ready-to-use scripts for importing issues from various trackers. We also provide a script that imports issues to YouTrack from a CSV file. This script lets you import issues from any other issue tracker that exports issues in CSV format.