Can I claim my granddaughter as a dependent?

It depends.  By the way, congratulations on your granddaughter!

You may claim your granddaughter if she is your Qualifying Child or Qualifying Relative  (she likely is not your qualifying relative).  You can claim her as a qualifying child if:

1. She lived with you at least 6 months and 1 day in 2016.  (Note:  The IRS considers her to have lived with you all year if, after she was born, she lived with you the remainder of the year.)
2. She did not provide at least half of her own support (I think that is a safe assumption).
3. Her mother will not claim her (you lose the tiebreaker automatically in that case).
4. You have more earned income than her mother (your daughter).

If your daughter lives with you and you are allowed to claim your daughter, you automatically qualify to claim your granddaughter as well because someone who is a dependent cannot claim a dependent.  Here is a link to the IRS' definition of a Qualifying Child for more information.