No, it can't. No way.
It would be totally illegal.
The Federal Reserve, nor any central bank, doesn't have the power to create a new currency. It's duty is to protect, or control, or develop (depending on circumstances) the currency which is legal tender in the country. It cannot create a new currency, and it cannot change the currency it's working with.
They could if they just said that they were "reformatting" the way that the USD is transacted within the banking system and that they are moving to a USDCoin that essentially just takes over the place of the physical USD and digital USD in bank account.
They could also create an addendum to the current laws and they would sell the addendum as "we need to adapt the law to the current advances in cryptocurrencies that are among us".
The real question becomes this: IF the fed did create their own coin, would you trade all of your bitcoins in for them? I don't think so...
Also they could create "fake" hard caps to the currency and then they would need to hardfork it every few years to increase the cap, much like they need to vote on "increasing the debt ceiling" every few years...
Sorry, but the Federal Reserve cannot change any law. It can certainly look at cryptocurrencies, but it would require a vote from congress to allow it to change from paper money to virtual currency.