One experiment that was performed involved measuring the position of a star during a solar eclipse. The star was one whose position was accurately known. The position during the solar eclipse was such that its light just grazed the sun, which was obscured by the moon, so that the star could be observed. The star's apparent position was shifted from its known position due to the gravitational effect of the sun. I believe that this was the first experiment that was performed to verify Einsteins prediction.