Can placing rubber bands around calves help to increase blood supply to the brain?

No. It could help decrease blood supply to the calves though. Seriously, don’t waste your time with this - you’d be better off hanging upside down by the ankles…

If you really want to increase blood flow to the brain, try taking vinpocetine supplements, though if you’re already healthy it’s doubtful increased blood flow will accomplish anything. The body is optimized to provide the correct amount of blood and more isn’t always better. You might get a temporary mental boost, but excess oxygen can cause oxidative damage in the long run and the brain is very good at maintaining homeostasis and undoing the effects of anything you keep putting into it.