The Roe majority ruling of 1973 holds that the government has a legitimate interest in protecting potential human life, but that this does not become a "compelling" state interest--overriding the woman's Fourteenth Amendment right to privacy, and her subsequent right to terminate her pregnancy--until the point of viability, then assessed at 24 weeks. The Supreme Court did not state that viability is or is not when a fetus becomes a person; just that this is the earliest point at which it can be proven that the fetus has the capacity to have a meaningful life as a person.
The Planned Parenthood v. Casey Standard
In the Casey ruling of 1992, the Court scaled back the viability standard from 24 weeks to 22 weeks. Casey also holds that the state may protect its "profound interest" in potential life so long as it does not do so in a way that has the intent or effect of posing an undue burden on the woman's right to terminate a pregnancy prior to viability. In Gonzales v. Carhart (2007), the Supreme Court held that a ban on live intact D&X ("partial birth") abortions does not violate this standard.
In Fetal Homicide Statutes
Laws that treat the murder of a pregnant woman as a double murder arguably affirm fetal rights in a statutory manner. Because the attacker has no right to terminate the woman's pregnancy against her will, it could be argued that the state's interest in protecting potential life is unrestricted in cases of fetal homicide. The Supreme Court has not ruled on the matter of whether fetal homicide, on its own, may constitute grounds for capital punishment.
Under International Law
The only treaty that specifically grants rights to fetuses is the American Convention on Human Rights of 1969, signed by 24 Latin American countries, which states that human beings have rights beginning at the moment of conception. The United States is not a signatory to this treaty. The treaty does not require that signatories ban abortion, according to the most recent binding interpretation.
Most philosophies of natural rights would hold that fetuses have rights when they become sentient or self-aware, which presumes a neurophysiological definition of personhood. Self-awareness as we generally understand it would require substantial neocortical development, which seems to occur at or near week 23. In the premodern era, self-awareness was most often presumed to occur at quickening, which generally takes place around the 20th week of pregnancy.
Religious traditions holding that personhood rests in the presence of a non-physical soul differ with respect to the question of when the soul is implanted. Some traditions hold that this occurs at the moment of conception, but most hold that this occurs much later in the pregnancy, at or near quickening. Religious traditions that do not include belief in a soul do not generally tend to define fetal personhood in explicit terms.
The Future of Fetal Rights
The conundrum posed by abortion rests in the tension between a woman's right to terminate her pregnancy and the potential rights of the potential human being. Medical technologies currently under development, such as fetal transplantation and artificial wombs, could one day eliminate this tension, deprecating abortion in favor of procedures that terminate the pregnancy without harming the fetus.