Just as what you see in "Branches" page, there isn't any way to create branch with the Rest API. And mostly, you can only read/get the information with the Version Control API for now.
If you don't want use C#, you can automate the process with Powerhshell:
param(
)
begin
{
# load the required dll's
[void][System.Reflection.Assembly]::LoadWithPartialName("Microsoft.TeamFoundation.Client")
[void][System.Reflection.Assembly]::LoadWithPartialName("Microsoft.TeamFoundation.VersionControl.Client")
}
process
{
$server = New-Object Microsoft.TeamFoundation.Client.TeamFoundationServer("http://tfsserver:8080/tfs/DefaultCollection")
$vcServer = $server.GetService([Microsoft.TeamFoundation.VersionControl.Client.VersionControlServer]);
$changesetId = $vcServer.CreateBranch('$/Demo/Code/Main', '$/Demo/Code/Dev/Branch', [Microsoft.TeamFoundation.VersionControl.Client.VersionSpec]::Latest, $null, "New branch from script", $null, $null, $null)
"Branch created with ChangesetID: $changesetId"
}