Can concrete be poured in the rain?

No, inadvisable.

Too much water in concrete results in greater shrinkage, more cracks and a reduced compressive strength. Also, it is hard to get a good finish even if you can get a crew to stay and work it.

You can but you probably shouldn’t.

You string a tarp roof over the area held up by aluminum posts and work under it.

There’s a highrise being built right next to my building, and I’ve been watching their progress for the past several months. This is purely anecdotal, but I’ve never seen them pour concrete in the rain.

You can, but it’s a bad idea unless you want to be replacing that concrete in a few years.

There are forms of concrete that will harden adequately under water – they’re usually used for swimming pools. Of course, no one’s parking a tractor-trailer in a swimming pool.

I have seen it done as @Espiritus_Corvus mentions using a large “circus” tent over the work but is not very common and nobody likes to do it.
It is hard to plan for. You have to prepare ahead of time, have the tent ready for pickup and set up prior to the rains, inform the crews they will be working regardless of the weather, etc. Not really worth the headaches and additional costs associated with it. Not to mention it is always tons of fun pulling a stuck concrete truck out of the mud and if he hasn’t poured out, who gets stuck with the cost of the concrete? Who pays for replacement of the drum when the stuff hardens in it?

I was once passing a job on a university where they had dug a huge hole for the underground parking garage and were in the process of pouring the walls. They didn’t pour in the rain but got on it immediately afterward. Unfortunately the ground was too soft and as they backed another truck up too close to the edge, the edge caved in, the concrete truck slid down hind end first into the hole taking out the form work as it went. Fortunately the reinforcing in the walls stopped the truck from crashing tail first into the basement and thereby probably saved the drivers life but several days worth of work was totally ruined. In addition to tearing down a huge section of forms what concrete they had poured spilled out of the crushed and shattered mass of panels and steel adding to the overall destruction.

Rumor has it the job superintendent never took responsibility and called the cement plant and told them to come get their fully laden truck out of his jobsite.

There is a type of Concrete, called hydraulic cement which uses the water in the hardening reaction. Also known as Roman concrete; it has volcanic ash and slaked lime. Herod used it for his making of harbors underwater pilings by pouring cement right in the harbor