Marriage rights for inmate's vary depending on the state and even the sexual orientation of the prisoner. As of 2010, there are no rules or regulations regarding same-sex marriages within the prison system. Certain states, such as Alabama, do not permit conjugal visits. Following are the basic rights of marriage according to the 14th amendment. However specific rights, rules and regulations for marrying a person in the prison system can be obtained via the specific prison in which he or she is detained, as rules may vary depending on the needs of the institution, inmate behavior and state law.
Section One of the 14th Amendment is the part of the constitution that protects inmates' right to marriage. It declares that no state has the right to "deprive any person of life, liberty, or property, without due process of law." This means that not only can you not be deprived but also you cannot be discriminated against for poverty or imprisoned status. Basically, an inmate has the exact same rights as any citizens (note that "privileges" are not the same as "rights" and the definition may vary by state), so ultimately an inmate may marry but the process of gaining permission will vary depending on whether your state views marriage as a right or as a privilege.
The Right of the State
It is the state's responsibility to make judgments as to who and how a person can marry. According to the Cornell University Law School, marriage is defined as "The legal union of a couple as spouses. The basic elements of a marriage are: (1) the parties' legal ability to marry each other, (2) mutual consent of the parties, and (3) a marriage contract as required by law." This means that the parties may not already be married (except in those states where polygamy is legal) and must be of sound mind to enter into contracts legally (that is, appropriate permission if either party is a minor, etc. This protects those that have a mental incapacity or disability or are otherwise incapable of deciding for themselves). Marriage is regulated by the state and there remains a great deal of difference between state to state rights. Variables in how laws are imposed remain a daily fact.
The Defense of Marriage Act (DOMA) defined marriage as "only a legal union between one man and one woman as husband and wife" (1 U.S.C. § 7) and states that "no State, territory, or possession of the United States, or Indian tribe, shall be required to give effect to any public act, record, or judicial proceeding of any other State, territory, possession, or tribe respecting a relationship between persons of the same sex that is treated as a marriage under the laws of such other State, territory, possession, or tribe, or a right or claim arising from such relationship." This means that even though a same-sex marriage may be legal in one state, other states may choose not to recognize them.
The Right to Appeal
"The Congress shall have power to enforce, by appropriate legislation, the provisions of this article." This means that if your rights have been infringed, you can appeal them and that if a judgment is illegal it can be overturned.