  We propose a class of non-integrable quantum spin chain models that exhibit
quantum many-body scars even in the presence of disorder. With the use of the
so-called Onsager symmetry, we construct such scarred models for arbitrary spin
quantum number $ S $. There are two types of scar states, namely, coherent
states associated to an Onsager-algebra element and one-magnon scar states.
While both of them are highly-excited states, they have area-law entanglement
and can be written as a matrix product state. Therefore, they explicitly
violate the eigenstate thermalization hypothesis. We also investigate the
dynamics of the fidelity and entanglement entropy for several initial states.
The results clearly show that the scar states are trapped in a perfectly
periodic orbit in the Hilbert subspace and never thermalize, whereas other
generic states do rapidly. To our knowledge, our model is the first explicit
example of disordered quantum many-body scarred model.
