Activation cross sections of the natRb (d,xn)87m,85m,85g,83,82Sr, natRb(d,x)86,84,83,82mRb and natRb(d,x)85mKr nuclear reactions have been measured for the first time through an activation method combining the stacked foil irradiation technique and gamma-ray spectrometry. The provided cross sections from the present investigation are all new, in such a way contribute to the completeness of the experimental database. The experimental cross sections were compared with the theoretical prediction in the TENDL-2019 TALYS based library and with our calculation using ALICE-D and EMPIRE-D model codes in order the improve their predictivity. Thick target production yields were calculated form the new cross sections for all investigated radioisotopes. Practical applications of the results are shortly discussed.