None of Sweden's foreign missions in the US, including the embassy in Washington DC and the consulates general in New York, San Francisco and Houston, have the right to perform weddings.
The Church of Sweden performs weddings in several locations around the US. Read more about weddings at the Church of Sweden abroad Gifta sig utomlands - Svenska kyrkan
For information about the Swedish Church and weddings in Texas contact Mobil präst i Nordamerika
For information about American weddings (church or civil), contact the relevant American authority, usually a "Marriage License Bureau", in the state where you want to get married.
