As long as the air isn't damp out and the sun is shining then it should take from 24 to 48 hours for the fully stacked wood to dry out from the rain.
If you have wood sitting out stacked up then it's best to cover it with a tarp to prevent the rain from totally soaking the wood since when the wood gets too wet it could eventually warp the wood.
If it's firewood then warping doesn't matter but even covering it up with a tarp will prevent it from getting wet.
If the wood you have stacked is firewood you can bring some in and put it close to the stove to help speed up the drying process.
I have a rack behind my wood stove where I place wood that has gotten a bit wet and it helps to dry it out faster from the heat the wood stove puts out.