You could. Simple present perfect may imply it is no longer raining.

The continuous form put the emphasis on the 'action'. In this case, we're emphasising the action of the rain falling and possibly how long it was raining for. In this conversation, the present perfect continuous is the most natural form to use. We'd use the simple form in a sentence such as 'It's rained nearly every day this month'. This focuses not on the action of rain falling, but on the total number of rainy days that have occurred over recent weeks.