“You shall not make any cuts in your body for the dead nor make any tattoo marks on yourselves: I am the LORD.” (Leviticus 19:28)
Also, the Bible specifically advises the Christian woman to be modest:
“Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments” (1 Timothy 2:9)
Just think how much a tattoo or a piercing is modest and discreet…
Actually, the tattoos and the body piercings are made in order to draw attention to the outward appearance, while the Bible advises the exact opposite:
“whose adorning let it not be that outward one of tressing of hair, and wearing gold, or putting on apparel; but the hidden man of the heart, in the incorruptible [ornament] of a meek and quiet spirit, which in the sight of God is of great price.“ (1 Peter 3:3-4)
“Do ye not know that your body is [the] temple of the Holy Spirit which [is] in you, which ye have of God; and ye are not your own? for ye have been bought with a price: glorify now then God in your body.“ (1 Corinthians 6:19-20)
“I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service.“ (Romans 12:1)