For a solid sphere - Absolutely not!
This calculation from http://www.aleph.se/Nada/dysonFAQ.html explains why:
8) How strong does a rigid Dyson shell need to be?
Very strong. According to Frank Palmer:
Any sphere about a gravitating body can be analysed into two hemispheres joined at a seam. The contribution of a small section To the force on the seam is
$\mathbf{g}\text{(ravity)}\cdot\mathbf{d}\text{(ensity)}\cdot\mathbf{t}\text{(hickness)}\cdot\mathbf{A}\text{(rea)}\cdot\mathbf{cos}(\text{angle})$.
The integral of $\mathbf{A}\cdot\mathbf{cos}(\text{angle})$ is $\mathbf{\pi}\cdot\mathbf{R^2}$.
So the total force is $\mathbf{g}\cdot\mathbf{d}\cdot\mathbf{t}\cdot\mathbf{\pi}\cdot\mathbf{R^2}$. Which is independent of distance, neatly enough.
The area resisting the force is $2\cdot\mathbf{\pi}\cdot\mathbf{R}\cdot\mathbf{t}$.
Thus, the pressure is $\mathbf{g}\cdot\mathbf{d}\cdot\mathbf{R}/2$; this can be translated into a cylindrical tower of a given height on Earth. If that tower built of that material can stand, then the compression strain is not too great.
At 1 AU, that comes to $2\cdot(\mathbf{\pi}\cdot\text{AU}/\text{YR})^2$, or -- by my calculations -- in the neighborhood of 80 to 90 THOUSAND kilometers high.
For the thin version held up by solar wind and photon pressure - nope. The numbers are better but still out of our reach.
For the swarm of independent solar panels - yes. We would just need to build a hell of a lot of them - might need to take apart a small planet for raw materials though...