  Scanning-probe magnetometry is a valuable experimental tool to investigate
magnetic phenomena at the micro- and nanoscale. We theoretically analyze the
possibility of measuring magnetic fields via the electrical current flowing
through quantum dots. We characterize the shot-noise-limited magnetic-field
sensitivity of two devices: a single dot in the Coulomb blockade regime, and a
double dot in the Pauli blockade regime. Constructing such magnetometers using
carbon nanotube quantum dots would benefit from the large, strongly anisotropic
and controllable g tensors, the low abundance of nuclear spins, and the small
detection volume allowing for nanoscale spatial resolution; we estimate that a
sensitivity below $1 \, \mu\text{T}/\sqrt{\text{Hz}}$ can be achieved with this
material. As quantum dots have already proven to be useful as scanning-probe
electrometers, our proposal highlights their potential as hybrid sensors having
in situ switching capability between electrical and magnetic sensing.
