Best answer: Yes you can mine cryptocurrency with a Raspberry Pi. However, it's extremely difficult to turn any profit as the cost of electricity can outweigh the return due to the Raspberry Pi's relatively low performance when calculating hashes.
Amazon: Raspberry Pi 3 B+ ($40)
An exercise in counterproductivity
Cryptocurrency is "mined" by calculating complex equations on a computer. Any modern computer — even a smartphone — can be used to mine coin, but the hard part is mining enough of it to make things worthwhile.
Cryptocurrency value usually works on two sliding scales; as more is mined it becomes tougher to mine more and the value increases. However, these scales aren't equal and even though the value may skyrocket, the complexity of mining them has skyrocketed more. Today, mining popular cryptocurrencies like Bitcoin on a Raspberry Pi would cost more in electricity that you would earn in profit.
You could, in theory, mine newer coin that hasn't become as popular. this means it's easier to find new coin but it also means the value is lower. Should a new currency follow the trend we've seen from currencies like Bitcoin or Ethereum, the few pennies of profit you make each day could turn into quite the sum of money in the future.
Mining cryptocurrency with a Raspberry Pi can be fun, but that should be the only reason you try. It's simply not profitable.
Raspberry Pi 3 B+
The welcome version bump
With its1.4GHz 64-bit quad-core processor, dual-band wireless LAN, and integrated PoE (Power over Ethernet), this is the version bump that Pi enthusiasts need.