Of course, we can't fly a magnetometer next to an exoplanet to measure the magnetic field, but might it be possible to find indirect evidence (e.g. polar auroras) of a magnetic field generated by an exoplanet? Has this already been done?
You usually look for electronic synchrotron emission in the radio, which corresponds to the magnetic field strength expected for giant planets. There has been a single detection claimed with LOFAR by Turner et al., (2020) around $\tau$ Bootes, but it's very noisy and hence disputed.
Other effects like Zeeman-splitting have been considered for detection, but require clean, high-resolution signals from planets. So far this is too difficult to perform due to stellar contamination.
Magnetic field searches around brown dwarves have been more successful, but those are not planets, of course.
Magnetic fields can be measured via the Zeeman effect, thus a change of absorption and emission lines in spectra - a shift which depends on the direction and the strength of the magnetic field. This is a method commonly employed to measure and map the magnetic field of the Sun (also here).
The difficulty in doing so is the necessary precision in the spectral data of the source and the ambiguity if you sample over a broad area where this effect is also convoluted with the doppler broadening due to mapping areas with different relative speed towards the observer. Generally, getting high-resolution spectral data requires much light or long exposure, both of which can be difficult to obtain for exoplanet atmospheres. I'm not aware of magnetic field measurements on exoplanets so far, yet it might become viable in the future. It is done for stars.