It is customary for a Sephardic groom to be called up for an aliyah and recite a blessing over the Torah on the Shabbat after his wedding. After the groom’s aliyah, the congregation will often sing “Siman Tov u’Mazal Tov” to him.
Both the Shabbat Chatan and the Aufruf are customs that are based on a Talmudic source that records that King Solomon built a special gate for bridegrooms–who would pass through it on Shabbat to be greeted and blessed by family and friends. After the destruction of the Second Temple, the custom was moved to the synagogue.
*Please note that the Shabbat Chatan is a special custom of the Sephardic community and is not generally celebrated by Ashkenazim. However, newly married Ashkenazi men are usually called-up for an aliyah in the synagogue after their wedding, as well.