  We present an experimental study of macroscopic and microscopic magnetic
anisotropy of a spin tetramer system SeCuO$_3$ using torque magnetometry and
ESR spectroscopy. Large rotation of macroscopic magnetic axes with temperature
observed from torque magnetometry agrees reasonably well with the rotation of
the $\textbf{g}$ tensor above $T \gtrsim 50$~K. Below 50~K, the $\textbf{g}$
tensor is temperature independent, while macroscopic magnetic axes continue to
rotate. Additionally, the susceptibility anisotropy has a temperature
dependence which cannot be reconciled with the isotropic Heisenberg model of
interactions between spins. ESR linewidth analysis shows that anisotropic
exchange interaction must be present in SeCuO$_3$. These findings strongly
support the presence of anisotropic exchange interactions in the Hamiltonian of
the studied system. Below $T_N=8$~K, the system enters a long - range
antiferromagnetically ordered state with easy axis along the $<\bar{1} 0 1>^*$
direction. Small but significant rotation of magnetic axes is also observed in
the antiferromagnetically ordered state suggesting strong spin-lattice coupling
in this system.
