Is there any hardware available to calculate single sha256 hash? I'm looking for a hardware that can generate sha256 hash of the input.
Sure, designs for such chips are available on the internet (e.g. http://www.cast-inc.com/ip-cores/encryption/sha-256/cast_sha256.pdf) but you would probably have to integrate them yourself into a hardware module, which is going to be expensive and time-consuming. You will find those integrated in things like HSMs and cryptographic accelerators as well as mining modules (e.g. bitcoin miners), but it's unlikely you will find a fast, cheap, standalone IC specifically dedicated to computing SHA-256 hashes from an arbitrary input.

The reason is simple: bandwidth. Take bitcoin miners for instance, very little bandwidth is required, since the device can mine autonomously without a constant stream of data from the host (it's just searching for a block that hashes to a specific number of zeroes, so it can just hash an incrementing counter, for instance). But a general purpose SHA-256 hashing device would need to be fed data from the host, meaning it can only run as fast as the communication interface, which is necessarily going to be limited to a few gigabits per second, maybe a few tens of gigabits per second in the best case.

If this device is to communicate with a computer, USB is a no-go as it is too slow (it wouldn't be much faster, if at all, than just running SHA-256 on all cores of a modern CPU, for instance). Probably your best bet is to leverage PCI express 3, or maybe Thunderbolt, that would be fast enough to make it worth it. So you could make a "SHA-256 card" that is designed or at least programmed to compute SHA-256 hashes, and plug it into a PCI express port to start sending it data.

Guess what: such a device already exists, and is called a GPU. This is, by very, very far, the most cost effective hardware to perform SHA-256 hashes over arbitrary inputs, in terms of raw performance. It's also commodity hardware, which helps, and is quite straightforward to program for, as opposed to FPGAs. It's not designed only for hash calculations, but it's as close as you're going to get to that if you don't want to start doing some serious (and expensive) R&amp;D with high-performance, expensive FPGAs and ASICs.