The word raj is related to English words like "regal" and "reign" which are derived from Latin rex (reg-). Both Sanskrit rajan, "king," and Latin rex come from the same Indo-European root, *hreg-.
You may have seen the television miniseries The Jewel in the Crown which is based on the four-volume novel series known as The Raj Quartet; The Jewel in the Crown is title of the first novel in the series.