Yes, it's income, and from that point on you own it with a cost basis of that same income value on that date. So when you sell/spend it in the future you will use that work out the different as being your gain (or loss).

So, if you received 1 BTC yesterday, you report $365 income. (you can choose to use any reliable and consistent exchange rate source). If you sell it in a month for $400, you also have to report $35 short-term capital gains...which is taxed as income. If you sold it for $300 in a month, you could declare a loss of $65, which can be offset against your income, so reducing your tax bill.