Is there a map with all state legislative voting districts? In other words, is there a single map which contains all of the districts which elect representatives to the lower state house, and a single map which contains one to the upper state house (often called the Senate).
It wouldn't be practical to have a national map of all state legislative districts. Not only do many states have two sets of different, overlapping districts, but the districts would often be too small to show on a national map.
Some of the relevant Wikipedia pages have maps. E.g. for the Arkansas House:
That's a high resolution image for one state and notice how some of the urban districts are difficult to see. That only gets worse in more densely populated cities. And then expand it out to a national map. It's not practical.
Googling for "Alabama state senate districts" finds this PDF.
The national census site has maps. They look to be maps of each individual district: https://www.census.gov/geo/maps-data/maps/reference-sld2014.html
It seems conceivable to compile the state maps into two national maps, one for the upper chambers and one for the lower chambers. There would be some gaps as some state legislatures are unicameral (only one chamber). But I don't see any sign that that has already been done. And as I said, they wouldn't be particularly readable in urban areas.
I found http://sunlightlabs.github.io/openstates-api/ which is exactly what I was looking for