No official abbreviation, either three-letter or one-letter , has been assigned to it so far, although the JCBN/NC-IUBMB Newsletter 1986  refers to the paper by Günzler et al.  where Sec was used as the three-letter symbol and X as the one-letter symbol for the amino acid. Sec was considered as a useful addition to the approved list of amino-acid symbols while X required definition with each use because in general it means  an amino acid of unknown (or other) nature.
We now recommend both a three-letter and a one-letter symbol to be added to earlier recommended symbols (sections 3AA-1, 3AA-14, 3AA-15, and 3AA-21 of ), namely Sec and U. Although genes involved in selenocysteine synthesis and incorporation into proteins are designated with Sel, e.g. SelB for selenocysteine translation factor, SelC for selenocysteine-specific tRNA, SelD for selenide, water dikinase (selenophosphate synthase), the symbol Sec is preferred because it appears commonly in the symbol for the appropriate transfer RNA, i.e. tRNASec, and in abbreviations, such as SECIS (selenocysteine insertion sequences).
For the one-letter symbol, J and U can be considered but J is used in NMR work as designation for signals assigned either to leucine or to isoleucine which cannot be distinguished from each other. Therefore U remains as the best letter to designate selenocysteine. It is a disadvantage that U also stands for uracil, but analogous doublets exist for all the purine and pyrimidine bases: A = adenine or alanine; C = cytosine or cysteine; G = guanine or glycine; T = thymine or threonine.
To summarize, we recommend Sec as the three-letter symbol, and U as the one-letter symbol, for selenocysteine.
1. IUPAC-IUB Joint Commission on Biochemical Nomenclature, 1983, Nomenclature and symbolism for amino acids and peptides. Recommendations 1983, Biochem. J., 1984, 219, 345-373; Eur. J. Biochem., 1984, 138, 9-37; 1985, 152, 1; 1993, 213, 2; Internat. J. Pept. Prot. Res., 1984, 24, following p 84; J. Biol. Chem., 1985, 260,14-42; Pure Appl. Chem., 1984, 56, 595-624; Amino Acids and Peptides, 1985, 16, 387-410; Biochemical Nomenclature and Related Documents, 2nd edition, Portland Press, 1992, pages 39-69; and www.sbcs.qmul.ac.uk/iupac/AminoAcid/.
2. JCBN/NC-IUB Newsletter 1986. Arch. Biochem. Biophys. 1986, 244, 393-395; Biochem. Internat. 1986, 12, following p. 180; Biochem. J. 1986, 233, I-III; Biol. Chem. Hoppe-Seyler, 1986, 367, 1-4; Biosci. Rep., 1986, 6, 121-125; Chem. Internat. 1986, 8(4), 30-31; Eur. J. Biochem. 1986, 154, 485-487.
3. Günzler W.A., Steffens G.J., Grossmann A., Kim S.-M. A., Ötting F., Wendel A. and Flohé L. (1984) Hoppe-Seyler's Z. Physiol. Chem. 365, 195-212.