No, the Saffir-Simpson Hurricane Wind Scale currently tops-out at Category 5.
Snopes has also covered this issue:
Is Irma a Category 6 storm?
We can say with certainty that Hurricane Irma is not a Category 6 storm and will not become one because that category does not exist. The highest rating on the Saffir-Simpson Hurricane Wind Scale is a five, which contains all storms with sustained winds greater than 157 mph.
The idea that Irma is a Category 6 storm seems to have originated with a a blog post that implied that a new category, Category 6, would be created for Irma. While the post does not state this directly, its headline reads “Category 6? If Hurricane Irma Becomes The Strongest Hurricane In History, It Could Wipe Entire Cities Off The Map.” That story, written by end-time enthusiast and Republican candidate for Idaho’s first congressional district Michael Snyder, was first published on his blog “The Economic Collapse” before being aggregated by other clickbait websites.
Until a Category 6 is defined, there cannot be a Category 6 hurricane.