A computational finite element based technique is proposed for developing a stochastic reduced order model for rotating bladed disc with spatial random inhomogeneities. The spatial inhomogeneities imply the system to be randomly mistuned. The formulation assumes the availability of a high fidelity finite element (FE) model for the tuned system. The corresponding FE matrices are antisymmetric on account of the Coriolis forces due to rotation. The spatial inhomogeneities, available from limited point measurements on the blades, are modelled as non-Gaussian random fields with arbitrary distributions. A low order stochastic computational model is developed by projecting the FE model onto a reduced dimensional state space defined in terms of specified observable nodal points and expressing the stochasticity through an arbitrary polynomial chaos (aPC) basis. This model enables probabilistic quantification of the variabilities in the system response and estimating failure probabilities. The methodology enables drastic reduction in the state space and stochastic dimensions, addresses the practical difficulties with having limited measurable data points, antisymmetric FE matrices, aPC representation in complex irregular geometries and carrying out probabilistic analyses on industrial systems, at significantly reduced computational costs. The methodology is illustrated through an academic rotor and an industrial rotor blade.