Num 20:8-9 "Take the rod; and you and your brother Aaron assemble the congregation and speak to the rock before their eyes, that it may yield its water. You shall thus bring forth water for them out of the rock and let the congregation and their beasts drink." 9 So Moses took the rod from before the LORD, just as He had commanded him;
I have always understood this to be the same rod mentioned in Exodus 4-17, but it now appears more likely that it was Aaron's staff, which budded and was placed in the tent of meeting just a few chapters earlier in Num 17.
Num 17:10-11 But the LORD said to Moses, "Put back the rod of Aaron before the testimony to be kept as a sign against the rebels, that you may put an end to their grumblings against Me, so that they will not die." 11 Thus Moses did; just as the LORD had commanded him, so he did.
Most of my commentaries identify it as Moses' staff, and a quick google search showed me that there is a rabbinical tradition that the staff of Moses and the staff of Aaron are indeed the same staff, but I don't see that explicitly in the text anywhere.