Yes, there is! Bithereum (Bitcoin fork - https://bithereum.network/) uses Proof of Uptime (PoU) to reward anyone who runs a full node. This has been going on for over roughly 4 months and last week 186 full nodes were rewarded!

We just released a new tool called the Bithereum Node Tool which allows people to spin up a full node (pruned) with just 4GB of storage in just a few clicks of a button. We just posted our blog on PoU v2 with the node tool here: https://medium.com/bithereum-network/bithereums-proof-of-uptime-v2-0-69da7c1ca17