Is there way to see my progress percentage in Undertale?

There is no way in-game to view your progress percentage.

A good way to judge it is based on the number of areas in the game. There are 4 major areas in the game, and 6 bosses, all roughly evenly spaced. Using this, you can approximately figure out where you are in the game.

Undertale is a rather short game, and progress counters wouldn't necessarily be the most helpful thing in terms of game progression. Undertale is stylized in a way that you can feel when the end is nigh. But just saying, if you last fought a long-haired gal with gills and a penchant for aggressiveness , then you're about 50% done.

Just saying, LOVE isn't all there is to life.