So here is the problem. The electrification of the United States didn't happen in any sort of logical, or orderly fashion. It kinda just started cropping up. The earliest transmission lines drove street cars, and provided lighting and motive power to mines. Of course once you've laid the infrastructure for street cars, or ran a power line out to a rural mine, then regular consumers might as well tap into it. And so, by the time of the Depression, the populated areas of the US were pretty well wired, as well as small towns and such within reach of the big transmission lines. All well and good, it was easy, profitable and cheap to wire up these areas.

Running a 10 mile power line to Farmer Brown so he could run some electric lights and power his milking machine.... eh, not so much? Some farms had home generating plants, but not all of them, while other areas had rural electric cooperatives that ran lines to rural customers or might have owned a small generating facility. Still, the whole thing was a hodgepodge. Running power lines is expensive, and building any kind of quality line to rural areas was an expensive, and the cost of line construction fell to the customer. So needless to say, few people cared to pay for miles and miles of transmission line just for themselves.

Enter Roosevelt and the New Deal, and in 1935, the Rural Electrification Administration which operated alongside the Tennessee Valley Authority. In a nutshell, the REA provided low interest loans to promote the formation of rural electrical co-ops, and to construct the needful transmission lines. They also offered low interest loans to consumers to purchase electric appliances such as washers and cookstoves, which had the effect of "generating" (har har) profitable revenue for the local electric co-ops.

So to come back around to your question, finding or making such a map is unlikely, and would be a major undertaking, because rural electrification happened slowly, but steadily as the REA empowered rural residents and farmers to electrify over time, as opposed to a steady wave of electrification starting at point A, ending in Point B, and encompassing all points in between.

Tl;Dr. Rural electrification got off to a big start by the New Deal, and happened haphazardly across the nation as rural electric co-ops were formed and wired up their community.

EDIT: Aside from things that go bang, early transmission and telecommunications lines and the insulators used on them are more than a bit of a passion, I got happy when a mod pointed me to this question.

If you have a general interest in the cultural history of rural electrification in the South, the novel 'The Year the Lights Came On' uses the work of the Rural Electrification Administration as a plot device and setting.