From Greek σημαντικός, "significant" (= σημαντός "marked" + –ικός "–ic"; with σημαντός from σῆμα "sign" + –τός, a suffix forming verbal adjectives). Oxford English Dictionary.
The OED notes that semantic had a rare, obsolete use meaning "relating to divination through the interpretation of signs," with attestations as early as 1665.
The modern sense of "(relating to) the study of meaning in language" is much more recent, and is clearly a borrowing of French sémantique. The OED's earliest attestation of the English noun semantics in this sense is in Darmesteter (1886); of the adjective semantic, in Earle (1890).
The French word sémantique has some early uses connected to ciphers, military signaling, etc., but is attested in the sense of the study of meaning in language from 1874, in a review by "C. de G." of three Latin dictionaries (Centre National de Ressources Textuelles et Lexicales). I have been unable to identify who "C. de G." was; possibly Charles Graux.
Whoever "C. de G." was, there is no doubt that the term was popularized by Michel Bréal, who was a regular contributor to the journal where C. de G.'s review was published. CNRTL cites an 1879 letter from Bréal to Angelo de Gubernatis; Bréal's influential book Essai de sémantique was published later that same year.
From Bréal's work, the word passed into wider usage among linguists, philologists, and the general public. Its use by logicians seems to originate with Chwistek's (1922) use of the German term Semantik.
For more on the history of the word semantics, see Read (1948).
References
- Bréal, Michel (1897) Essai de sémantique. Librairie Hachette et Cie.
- Chwistek, Leon (1922) 'Über die Antinomien der Prinzipien der Mathematik', Mathematische Zeitschrift 14.236–234.
- Darmesteter, Arsène (1886) The Life of Words as the Symbols of Ideas. Kegan, Paul, Trench and Co.
- Earle, John (1890) English Prose: Its Elements, History and Usage. Macmillan.
- G., C. de (1874) Review of Vanicek, Etymologisches Wörterbuch der lateinischen Sprache and two other Latin dictionaries, Revue critique d'histoire et de littérature 32.81–85, 33.97–102.
- Read, Allen Walker (1948) 'An Account of the Word "Semantics"', Word 4.2.78–97.