No. The filter stack directly in front of your camera's sensor already has a UV filter. The purpose is not to protect the sensor from anything, though. The sensor does not need protection from UV light. The purpose is to prevent UV light from negatively affecting the appearance of the image.

Whether a UV or other protective filter actually provides a protective benefit is a hotly debated topic. Because a thin flat filter is more likely to shatter than a thicker and differently shaped front element made of different materials, there are cases where a shattered filter may actually increase the amount of damage to a lens' front element by causing multiple scratches. One must also consider the optical penalty imposed by adding two more air/glass interfaces into the optical path. Just how detrimental that will be depends on the specific shooting conditions as well as the overall quality of the specific filter and its coatings.

For more about the overall subject of To filter or not to filter (for lens 'protection'), that is the question, please see the following questions here at Photography at Stack Exchange:

is it normal to get significant lens flare with a 50mm f/1.8 prime lens?
Will a filter cause more or less damage when lens is dropped?
How do I remove a broken/warped UV filter from my lens?
Do cheap filters have an effect on image quality?
Front element shattered, can I have my lens repaired?
What kind of filter (if any) should I use when photographing a theater scene?
Does high reflectiveness of digital sensor lead to poor lens performance?
How durable are external lens coatings?
Can incense damage a lens?
What could cause this visible artifact which seems to a be a glowing inverse of something outside of the frame overlayed on this photograph?
Is a UV Filter required/recommended for lens protection?
Are there any downsides to using a good-quality UV filter?
What is the downside of a cheap UV filter that is used solely for the protection of the lens?
Does the quality of a UV filter make a difference when used with a cheap lens?
What effect does a UV filter provide?
Should I put UV filter to protect the lens even if I put a lens hood?
"Filters must be destroyed!" (Must every UV/protection filter question get this response?)

Beyond our site here, there is a good series of blog articles by Roger Cicala, founder and chief lens guru at lensrentals.com, that addresses the issues surrounding using filters for protection. They are presented below in chronological order.

The myth of UV filters
The Glass in Front of Your Glass: All About Filters
Good Times with Bad Filters
Front Element Lens Protection Revisited
Yet Another Post About My Issues With UV Filters
My Not Quite Complete Protective Filter Article