The fine structure constant can be measured in two different ways.
One is to measure the g-factor of the electron in a Penning trap. This can be related to the fine structure constant using quantum electrodynamics (QED).
The other is to measure the recoil that an atom receives when it absorbs a photon in an atom interferometer. By combining the result with another well known constant, the fine structure constant can be calculated.
The results of both methods agree to 12 digits, which shows that the QED calculations of the electron g-factor are correct on that level.
