Yes, you can two Immovable Rods as an infinite ladder or monkey bars, and it's really cool.
This flat iron rod has a button on one end. You can use an action to press the button, which causes the rod to become magically fixed in place. Until you or another creature uses an action to push the button again, the rod doesn’t move, even if it is defying gravity. The rod can hold up to 8,000 pounds of weight. More weight causes the rod to deactivate and fall. A creature can use an action to make a DC 30 Strength check, moving the fixed rod up to 10 feet on a success.
It's certainly reasonable to try holding each rod in one hand in such a way that your thumbs are on the buttons, so that you can alternately release and engage the rods. As a rod is released, you could swing forward holding onto the fixed rod, and engage the free rod, thereby propelling yourself across the moat. You could do the same thing to climb vertically, although you'd be doing a one-handed pull-up as you moved each rod. The GM might impose strength, dexterity, or even constitution checks along the way. Depending on the distance and other factors, fatigue might become a serious issue. Particularly annoying is the description of it being a flat iron rod. Wrapping it with leather to make handgrips might be more comfortable.
There might be easier ways.
If you don't want to cling to the darned things while you're trying to push the buttons on the ends, you can tie a rope and a stirrup to each. Then stand in the stirrups and alternately activate the rods.
No matter what, it's going to be slow, because it'll most likely take a turn per activation. It could take a long time to go very far.
A little invisibility might help with getting spotted as you dangle by your arms over the shark-infested moat picked out by spotlights.
Up here in the castle we've got boxes of those things. We resell 'em down in the thieves' quarter. You wouldn't believe the number of would-be anti-heroes who try to get over the walls that way. Sometimes we get several a night. We generally roll dice as to whether to use fireball, heat metal, or grease. Sometimes we just lasso them. If it's slow we use a mage hand to mess with the buttons.
Then there was the guy who was so strong he didn't bother with pressing the buttons. He'd just keep pulling on the things til he'd get them to move. That dude was no fun at all once we got him on deck. Serious attitude problem.
Then there was the assassin who got past us somehow and nailed a visiting duke. We think she was using those rods, but we're not sure. She must have had some other trick up her sleeve.
Yeah, between the yahoos with the immovable rods, the flyers, the spider climbers, the monks, the thieves, the polymorphed lizards, the familiars, the invisible flying carpets and everything else, it gets pretty busy up here. One night we had so many we almost ran out of charges on the gems of seeing.