How does one measure vector magnetic field of astrophysical object? Magnetic field strength is measured using Zeeman splitting. This is the one of the way Sun's magnetic field strength is measured. Now, how one measure vector magnetic field?
Vector magnetic field = Magnetic field and it's components.
Using spectropolarimeter one can measure vector Magnetic field.

A spectropolarimeter based on a ferroelectric liquid-crystal modulator is described. An optical system with spatial modulation of the positions of the components of Zeeman splitting is a specific feature of this instrument. In comparison to the familiar instruments, the developed spectropolarimeter utilizes the light flux more efficiently and contains only one photodetector array. An operating spectropolarimeter developed at the Sayan Solar Observatory is considered as an example. Comparative estimates of noises in different operating modes are presented.

(Ref: Kolobov, D.Y., Kobanov, N.I. &amp; Grigoryev, V.M. Instrum Exp Tech (2008) 51: 124. https://doi.org/10.1134/S0020441208010156)