Yes, but it may depend on your setting.
There may be several reasons for someone to wear a mask, other than attempting to hide their identity for suspicious reasons, but you'll need to discuss which are viable with your DM. Here's a few I can think of off the top of my head:
1. Your character is part of (or pretending to be part of) an organized group that keeps their faces covered as part of their beliefs.
Ask your DM if there are any such groups in your setting. They may be a religious group or cult, but don't necessarily have to be. Perhaps a famous band of mercenaries or order of knights is well known for always keeping their faces covered to help intimidate their enemies. Your character may have joined one or simply stolen or otherwise acquired a mask similar to the ones worn by such a group. This would offer a simple, believable explanation of why they keep their face covered.
2. Bluff about #1.
Maybe there are no groups known for covering their faces in your setting, rendering option 1 invalid. But...if your character claims that such a group exists in a faraway land, people with no knowledge of such distant places might buy it. If you can sell the story and your DM rolls with it as you get to higher levels, people might start recognizing you as a member of a non-existent order that you only made up to explain your mask.
3. Your character is known as an entertainer or artist who never removes their costume. Consider the Entertainer or Charlatan background. Perhaps your character has chosen to hide in plain sight by being more flamboyant, thus attracting positive attention toward their mask. They allow the mask to be seen as only one of an artist's many eccentricities, to the delight (rather than suspicion) of the crowd. When not performing, your character can merely wave off interest and tell people they'll have to wait for the next performance.
4. Be upfront about it. This may not always work, but at least with your adventuring comrades it may be simplest to just tell them why you wear the mask. Have your character let the rest of the party know from the start that they wear it to cover their scars. Your party may be a bit suspicious at first, but once you've covered their backs in combat a few times, they'll probably accept it as a harmless quirk of a reliable comrade.