Did you try with rigid body constraints and 2-node springs (Spring between two nodes) ? They can work as torsional springs if attached to ROT NODE of a rigid body.
Other possibilities include *COUPLING with *KINEMATIC or *DISTRIBUTING (handles rotations unlike *DISTRIBUTING COUPLING), *EQUATION or even *MPC (not as good as in Abaqus though).
CalculiX doesn’t really have true rotational DOFs and there are issues with them but some workarounds involving the aforementioned keywords are available depending on the case.