Trumpler was the son of an industrialist. He studied at the university in his native city of Zurich in Switzerland (1906–08) and then at the University of Göttingen in Germany, where he obtained his PhD in 1910. After spending four years with the Swiss Geodetic Survey he emigrated to America in 1915, where he worked first at the Allegheny Observatory near Pittsburgh before moving to the Lick Observatory in California in 1919. He remained there until his retirement in 1951, also holding from 1938 to 1951 a professorship of astronomy at Berkeley.

Trumpler's most important work was his discovery in 1930 of conclusive evidence for interstellar absorption. He had examined over 300 open clusters of stars and found that remote clusters seemed to be about twice the size of nearer ones. He could find no observational error nor could he believe that he was witnessing a real phenomenon. He did, however, appreciate that this could be due to the presence of an absorbing medium occurring between the clusters and the observer on Earth. Trumpler assumed correctly that the quantity of absorbing medium increased with distance so that this would cause more distant clusters to appear fainter and would lead to an overestimate of their distance and size. For nearby objects only a small correction would be needed but for distant ones it could be quite considerable. He went on to estimate the effect of the absorbing medium, which was interstellar dust, on the dimming of the received light as 0.2 of a magnitude per thousand light-years. This means that the brightness of a star is decreased by interstellar dust by a factor of 1.208 for every thousand light-years that the starlight travels toward Earth. This had far-reaching implications for the work of such astronomers as Harlow Shapley who had been working on the size and structure of our Galaxy. It forced him to reduce the scale of his model by a factor of three.

Trumpler was also involved in 1922 in a test of Einstein's general theory of relativity. Einstein had predicted the amount by which starlight would be bent when it passed close to the Sun's limb. Trumpler assisted W. W. Campbell of the Lick Observatory to make the relevant measurements at Wallal in Australia during the total solar eclipse of 1922. The value they obtained for the deflection, 1.75 ± 0.09 seconds of arc, was much more accurate than the value Arthur Eddington had found in 1919 and was very close to Einstein's prediction of 1ʺ.745.