Wilhelm Conrad Röntgen is credited as the discoverer of X-rays. We'll give him that title; but Tesla wasn't far behind.
In 1894, Tesla began investigating "invisible" radiant energy after film in his lab was mysteriously damaged in previous experiments. It would later be confirmed that X-rays were the culprit, but Tesla suffered a major setback in March of 1895 when a fire in his laboratory tragically destroyed about $50,000 (again, the modern equivalent of over $1 million) worth of equipment and research. Did this lead to Röntgen beating him to the punch on discovering X-rays in November of 1895? We don't know, but it's safe to say that Tesla would have eventually figured it out.
After Röntgen's discovery, Tesla proceeded to experiment on X-ray imaging, and actually had some incorrect beliefs about X-rays. Nonetheless, he was still an early pioneer of X-ray imaging research.
As Bernard of Chartres said, and Isaac Newton paraphrased, "If I have seen further it is by standing on the shoulders of giants."
Scientific advances can rarely be attributed to a single inventor, and it's important to keep in mind the groundwork and ideas laid out in the past that have led to future innovation. As you can see, Tesla has had a bigger hand in a lot of modern technology than most people realize. For more on Tesla, we recommend checking out this info-comic.