Select the INCORRECTLY spelt word.

The correct option (the word that is incorrectly spelt) is Acceptible.

Let's analyze the spelling of each option:
1. Dearth: This is spelt correctly. It is a noun that refers to a scarcity or lack of something.
2. Acceptible: This is spelt incorrectly. The correct spelling is Acceptable, which ends with the suffix "-able" rather than "-ible". It is an adjective that means capable of or worthy of being accepted.
3. Corrupt: This is spelt correctly. It refers to dishonesty, bribery, or deviation from a sound state.
4. Barely: This is spelt correctly. It is an adverb meaning only just, scarcely, or by a very small margin.

Therefore, Acceptible is the incorrectly spelt word.