developer/api/v1/versions/Publish-Version.ps1

function Publish-Version
{
    param(
        [Parameter(Mandatory)]
        [string] $AppAlias,
        [Parameter(Mandatory)]
        [string] $VersionAlias,
        [Parameter(Mandatory)]
        [ValidateSet("Sandbox", "Published")]
        [string] $Stage
    )

    return Invoke-Api Post "/developer/api/v1/versions/$AppAlias/$VersionAlias/?action=promote&stage=$Stage"
}