When you get married, many things are joined together with your spouse such as your bank account, home, etc. One of the exceptions is an IRA. As the name implies, the account can only be associated with one individual.
Although you cannot share an IRA account, if your spouse does not work or earns a lower income than you, you may contribute to a Roth or Traditional IRA on their behalf. This will help increase tax-advantaged retirement savings for the whole family. The working/higher-earning spouse must be able to contribute to both accounts, and may even be able to make full contributions. Before doing so, double-check with your financial advisor since being married can affect income and tax deduction limits for IRAs.