Yes it is commonly used especially in the phrase “to gauge someone’s opinion”

Oscaaaaaaar! Sí, uso esta palabra cuando hablo de tratar de estimar algo. I need to gauge what the reaction of my boss will be. I could not gauge the distance between the two cars. The wire was not the correct gauge for the project. Además, a veces es un sustantivo. El panel dentro de tu auto que te dice cuánta gasolina tienes o qué tan rápido estás viajando; Estos son "gauges". Por cierto, este es un ejemplo de las reglas de ortografía totalmente locas en inglés. Lo pronunciamos así: wage, age, cage, etc. Y a veces incluso la escribimos así: gage ¡Buena suerte!

The noun, "a gauge" is common. It means a device that shows a measurement. A car has a fuel gauge, for example. The verb "to gauge" is much less common. It isn't a word I've used today. But it is NOT rare, or literary, or obscure, or technical, or academic. As you say, it means "to judge the amount of something." "Is this a good day to ask our boss to put a new computer into the budget?" "I don't know, I haven't gauged his mood yet." In deciding if words are reasonably common, I like to do a Google News search. News sources are in good written English, often copy-edited for usage and grammar, but not excessively formal. "Disney stock falters on day 2 of Bob Iger reboot as investors gauge CEO shuffle." Stock = accion en la bolsa. Falters = caerse un poco. CEO = director executivo. Investors are judging what the effect of the new director will be. "Doctor's office stress test could gauge your heart risk." The test could provide an approximate measure or indication of your heart risk. Despite the "U" in it, the word "gauge" rhymes with "age," "page," and "rage." It is not to be confued with the word "gouge," which means to scoop out something with a sharp tool.

It’s a common word with a number of meanings, but ‘guess’ is nearly the opposite. A gauge is a device that measures something. There’s a weather gauge at the train station. Use my thickness gauge on that sheet of metal. It’s a 22 gauge shotgun. The verb uses are derived from this idea. How can we gauge the interest in our new product? (measure it)