Thailand is one of a number of Buddhist countries around Asia that do not recognize same sex marriage, even though a same sex and transsexual relationships are allowed and accepted. Getting married is not allowed so if you feel that you would like to get a legal and binding Civil partnership to your same sex partner then you would travel to the UK were you can perform a civil partnership.
The British Embassy in Thailand issue a visa what they call a civil partnership visit visa. This type of visa is a 6 month visa and allows you to travel to the UK and marry with your Thai partner. They will then have to return to Thailand after a 6 month period. You must remember that the Civil partnership has to be booked and shown as part of the visa application.