Where does it say in G-d’s Torah that Women Must Always Have Their Heads Covered?

G-d’s Torah does not mandate for a woman to have her head covered at all times. It was customary for most women in the ancient Near East, Mesopotamia, and the Greco-Roman world to cover their hair when they went outside the home. In biblical times, women covered their heads with veils or scarves. The unveiling of a woman’s hair was considered a humiliation and punishment (Isa. 3:17; cf. Num. 5:18 on the loosening of the hair of a woman suspected of adultery; III Macc. 4:6; and Sus. 32).
In talmudic times, too, married women were enjoined to cover their hair in communal spaces (e.g., Ned. 30b; Num. R. 9:16). In a society so highly conscious of sexuality and its dangers, veiling was considered an absolute necessity to maintain modesty and chastity. If a woman walked bareheaded in the street, her husband could divorce her without repaying her dowry (Ket. 7:6). Some rabbis compared the exposure of a married woman’s hair to the exposure of her private parts (Ber. 24a), and forbade the recitation of any blessing in the presence of a bareheaded woman (ibid.). The rabbis praised pious women such as Kimhit, the mother of several high priests, who took care not to uncover their hair even in the house (Yoma 47a; Lev. R. 20:11). Nevertheless, covering the head was a personal imposition and restriction from which men were glad to be exempt. According to Sotah 3:8, men differ from women in that they may appear in public “with hair unbound and in torn garments.” In Eruvin 100b, one of the disadvantages or “curses” that is cited as an inevitable part of being female includes being “wrapped up like a mourner.” Some aggadic sources interpret this custom as a sign of woman’s shame and feeling of guilt for Eve’s sin (Gen. R. 17:8; ARN2 9; Er. 100b and Rashi ad loc.; cf., also, the opinion of Paul in I Cor. 11:1–16). Girls did not have to cover their hair until the wedding ceremony (Ket. 2:1). It gradually became the accepted traditional custom for all Jewish women to cover their hair (see Sh. Ar., EH 21:2
It is not commanded in G-d’s Torah that a woman have her head covered all the time. Many women today who are married, cover their hair as a sign of respect to their husbands, as the hair of a woman is her glory (1 Cor. 11:15). However, the Orthodox Jews do not subscribe to the authority of the B’rit Chadashah as equal to that of the Tanakh. In messianic Judaism we wear coverings at least in synagogue, as did the priests as they served in the Temple, and as a conscious reminder that we are under subjugation to our G-d. It is a sign of humility. Interestingly, you may often see in various Jewish communities, women who wear wigs to cover their hair, but the wigs are more attractive than their real hair! So, we must examine our motives if we choose to cover our hair and decide when and where we will choose to do so.
I hope this helps,
R. Davis