The chemical composition of the AISI Type 8620 compares with AWS 5.5 E8010-P1 weld rod (which is used for pipelines). Another choice of weld rod would be AWS 5.5 E10018M for the AISI Type 8620 base metal.
However, you need to determine the heat treatment condition of the AISI Type 8620 base metal before final selection of a weld filler metal. The mechanical strength properties of the weld filler metal can be as equally important as the base metal mechanical properties in certain applications. I would suspect that the pinion shaft would be heat treated (quenched and tempered), which requires careful selection of a weld filler metal.
Second concern is the preheat and post weld heat treatment requirements that need to be specified to assure minimal problems during and after welding. This would apply to the E8010-P1 weld rod that contains vanadium.