Sorry this is a bit techie, but iOS devices can use styluses, but they just input devices. Sorta like your finger but not as thick. Tons of folks will sell you some.
But that's only part of what you're asking. You also want a map you can draw on. Like highlighting a AAA map, no? you'd have to get a map you could import into a drawing/painting app, and then mark over it. I think some PDF apps would let you freehand draw over a PDF map as well.
But that's VERY different from what Google maps does. With that you are SELECTING a route, not DRAWING a route. It's a huge difference. Google has coordinates of roads stored and is smart enough to know you've chosen a particular road, and then sticks your route on top of it. VERY different than when you draw, like on that AAA map, where your highlighter is free to wobble all over, even right out into the ocean.
Unfortunately, the map app in iOS isn't as full featured as the desktop version, which can allow you to route all over the place, as long as Google recognizes a road there (not true for lots of backcountry stuff)
You could look at Trimble's Hunt and Fish nav app; I seem to recall that you can use an online web-based tool to draw routes that will snap to roads, and then download those routes to its nav app.
I haven't seen something that could allow you to create tons of routes on an iPad on one map view by dragging them around like you can do on a desktop. Sorry.
df Google search yields lots. Thanks.