Yes, DAY is a Scrabble word!

Letter values in Scrabble US: D 2, A 1, Y 4.

Is it a valid word?

DAY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

time for Earth to make a complete rotation on its axis
some point or period in time
a day assigned to a particular purpose or observance
the time after sunrise and before sunset while it is light outside
the recurring hours when you are not sleeping (especially those when you are working)
an era of existence or influence
the period of time taken by a particular planet (e.g. Mars) to make a complete rotation on its axis
the time for one complete rotation of the earth relative to a particular star, about 4 minutes shorter than a mean solar day
a period of opportunity
United States writer best known for his autobiographical works (1874-1935)

Also: twenty-four hours, twenty-four hour period, 24-hour interval, solar day, mean solar day, sidereal day, clarence day, clarence shepard day jr..