The crystal structure and magnetic properties of the RbMnPO4 zeolite-ABW-type material have been studied by temperature-dependent neutron powder diffraction, low-temperature magnetometry, and heat capacity measurements. RbMnPO4 represents a rare example of a weak ferromagnetic polar material, containing Mn2+ ions with T-N = 4.7 K. The neutron powder diffraction pattern recorded at T = 10 K shows that the compound crystallizes in the chiral and polar monoclinic space group P2(1) (No. 4) with the unit cell parameters: a = 8.94635(9), b = 5.43415(5), and c = 9.10250(8) angstrom and beta = 90.4209(6)degrees. A close inspection of the crystal structure of RbMnPO4 shows that this material presents two different types of zigzag chains running along the b axis. This is a unique feature among the zeolite-ABW-type materials exhibiting the P2(1) symmetry. At low temperature, RbMnPO4 exhibits a canted antiferro-magnetic structure characterized by the propagation vector k(1) = 0, resulting in the magnetic symmetry P2(1)('). The magnetic moments lie mostly along the b axis with the ferromagnetic component being in the ac plane. Due to the geometrical frustration present in this system, an intermediate phase appears within the temperature range 4.7-5.1 K characterized by the propagation vector k(2) = (k(x), 0, k(z)) with k(x)/k(z) approximate to 2. This ratio is reminiscent of the multiferroic phase of the orthorhombic RMnO3 phases (R = rare earth), suggesting that RbMnPO4 could present some multiferroic properties at low temperature. Our density functional calculations confirm the presence of magnetic frustration, which explains this intermediate inconunensurate phase. Taking into account the strongest magnetic interactions, we are able to reproduce the magnetic structure observed experimentally at low temperature.