How many weeks after having mononucleosis will i be able to go rock climbing again?

You can rock climb..: ....When you have fully recovered. Not somewhat recovered or mostly recovered, but fully recovered. That can take days, or it can take a couple of months.

Hard to speculate: For most, the process runs its course in 3 weeks, some 3 months. One feature you may want to verify before you climb would be to have them check your spleen. You should avoid any activity like contact sports or where falls are possible if your spleen is enlarged. This is common during mono. Trauma could make it rupture.