You can, but it is not very precise. The problem is that you cannot see the Sun and the background stars at the same time except during a total solar eclipse. You have to make the measurements either from two points on the Earth during a total eclipse and measure the shift in the Sun's position .This is hard, because at 93 million miles, even a 1000 mile difference between observers on the Earth, translates into only a 1000/93million x 206265 = 2-3 arc SECOND shift in the Sun's sky position. Then you have to take into account the gravitational bending of light of the stars near the Sun's limb too. Without an Eclipse, and being able to see the background stars, you have no sky reference markers that can be seen against the Sun's glare, and are capable of being measured to 2 arc second accuracy. The only exception is at radio frequencies, but even there the Sun is so bright and irregular in shape, that you still cannot get the required level of 2 arc second accuracy relative to distant radio sources.