Yes there are 7 trains a day between Bucharest and Constanta. Four of them leave from Gara de Nord station, three leave from Obor station. I'd recommend an InterCity or Rapid train; they take about 4 hours to get to Constanta.
You can look them up on this website of the Romanian Railways to see which one is more convenient for you:
(write Bucuresti Nord or Bucuresti Obor in the "From" field).
There are also flights between the two cities, see in the website of this Romanian air transport company:
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