  We develop an effective field theory (EFT) for deformed odd-mass nuclei.
These are described as an axially symmetric core to which a nucleon is coupled.
In the coordinate system fixed to the core the nucleon is subject to an axially
symmetric potential. Power counting is based on the separation of scales
between low-lying rotations and higher-lying states of the core. In leading
order, core and nucleon are coupled by universal derivative terms. These
comprise a covariant derivative and gauge potentials which account for Coriolis
forces and relate to Berry-phase phenomena. At leading order, the EFT combines
the particle-rotor and Nilsson models. We work out the EFT up to
next-to-leading order and illustrate the results in $^{239}$Pu and $^{187}$Os.
At leading order, odd-mass nuclei with rotational band heads that are close in
energy and differ by one unit of angular momentum are triaxially deformed. For
band heads that are well separated in energy, triaxiality becomes a subleading
effect. The EFT developed in this paper presents a model-independent approach
to the particle-rotor system that is capable of systematic improvement.
