Four
First Sunday in January 1962 is the 7th.
Years that will begin on a Sunday are 2017, 2023, 2034, 2040, 2045, 2051, 2062, 2068, 2073, 2079, 2090, 2096, 2102, 2108, 2113, 2119, 2130, 2136, 2141, 2147, 2158, 2164, 2169, 2175, 2186, 2192, 2197,...
January 21 would arrive on Monday, as expected. It would not cause a postponement of a presidential inauguration, if that is what you are wondering.
The next time will be 2012. Then 2017 and 2023.