Non-orthogonal multiple access (NOMA) is a promising technology for next-generation wireless communication systems due to its enhanced spectral efficiency. In this paper, we consider an uplink NOMA system operating together with a high-dimensional absorptive reconfigurable intelligent surface (A-RIS). We aim to minimize the total power transmitted by the users in order to meet signal-to-interference-plus-noise constraints at the base station in the presence of a jammer. We propose an iterative algorithm to solve the high-dimensional non-convex optimization problem using linear programming to find the transmit powers and a fractional programming algorithm based on the Dinkelbach algorithm with a sequential convex relaxation procedure to optimize the reflection coefficients. We show that our algorithm converges on large optimization problems, with a jammer comprising as many as $64$ antennas, and an A-RIS with $128$ elements. Our numerical results show that, compared with a standard RIS that reflects all impinging energy, the A-RIS can dramatically reduce the users' required transmit power and successfully mitigate interference from the jammer. The absorption capability of the A-RIS is in particular useful in cases when the number of jammer antennas is of the same order as the number of A-RIS elements.