Is there a certification or exam for Power BI offered by Microsoft? Yes - it is the DA-100: Analyzing Data with Microsoft Power BI. This exam will get you the Microsoft Certified Data Analyst Associate certificate. At the time of this writing, it is $165 to take the exam.
Here is the official site: DA-100 Exam
How difficult is the DA-100 exam?
I would say it's fairly difficult. An 8 out of 10 on a difficulty scale. For context, I've been the sole designer, publisher and admin of Power BI for the company I work for for about 4 years now (though I don't use it everyday). As the only developer, I need to have a solid understanding of the ins and outs of Power BI. I went into the test confident but was surprised at the difficulty of the questions (I did pass by the way).
As you may know, Microsoft is steering away from software skills and is now focusing on role based skills. Therefor, even if you know Power BI like the back of your hand, it's not guaranteed that you will do well on the test. For example, there are many (in fact most) questions pertaining to specific business scenarios where you need to choose the best solution - meaning all choices may be valid, but you are forced to consider situation as well.
How much should I study?
As mentioned before, I have 4 years of experience under my belt which provided a huge advantage. I only studied a few hours per day for about 1 week before the test. I basically just went through the Microsoft provided study material here, and also reviewed the official documentation. A word of caution though, this study guide does not go to the level of depth that some of the questions on the exam do.
What should I focus on?
Much of the exams material focuses on business related situations. For example:
Company ABC has X amount of data sources and has Y requirements.
The company needs to accomplish Z.
What solution best fits the companies needs?
There were quite a few questions on DAX as well. But it's not enough to know what CALCULATE() does. You should be very familiar with other functions and how you would nest them inside each other. Key functions would include: CALCULATE(), TOPN(), RANK(), FILTER(), SUMMARIZE(), RELATED(). Again, the questions don't ask you what they do. The questions are framed in a way where you need to know if these functions will accomplish what the business it trying to do.
I was surprised that there were not many Power Query questions - which was a bit disappointing for me since my Power Query knowledge is stronger than DAX. Even still, there was one question related to an M function that I had no idea existed until the exam. Indeed, I was hoping there would be more questions related to how Power Query functioned as a programming language but there were none.
Questions about permissions including RLS were frequent. You'll need to know admin related things like workspaces and how RLS can impact the organization's reports.
Finally, if you don't have experience with Power BI Pro then you will be at a disadvantage. A lot of questions are about things you will only have access to with a Pro license.
When will I know my results?
You results are displayed at the end of the test, so you will know whether you passed or failed as soon as you finish. This is both a blessing and a curse.
Hope this helps! And good luck if you are going to take it!