A router is overkill for doing a very slight roundover like this, although it will do the job well and very repeatably of course once you've dialled in the setting on the router or the router table.
As already described well in the Answer from @rob, you can do this sort of thing very well with a hand plane*, followed by light sanding with finer paper (whatever your finishing grit is). But not everyone has a hand plane or wants to get one so it's important to mention that you can do this simply by sanding alone.
This is one of the few times I'd recommend sanding as a viable shaping technique, but here it's appropriate since it's such an easy thing to do and it gives such good results. On an edge like this perhaps two passes with 80 or 100 grit paper (using a soft block or with the paper backed just by your fingers) followed by a couple of passes with 150 or 180 paper will give you very even, consistent results just about any time you need it.
No setup involved, just a few moments' work and after a quick dust off you're ready to apply finish.
*Doesn't have to be a block plane, they're just handy because they can be used one-handed with the work held by the other hand. Mind your knuckles doing this on narrow stock!