The way the sql server management studio and other big name tools like redgate do it, is to make a new temp table, copy the information over, then drop the old table (constraints & unique indexes first), rename the temp table to the old table name, then re-add any constraints and indexes. You really can't re-order what's already there.
Here's an example:
-- here's a sales table
CREATE TABLE [dbo].[Sales](
[SalesId] [int] IDENTITY(1,1) NOT NULL,
[Month] [int] NOT NULL,
[Year] [int] NOT NULL,
[InvoiceAmount] [decimal](15, 2) NOT NULL,
[SalesRepId] [int] NOT NULL,
[BranchId] [int] NOT NULL,
CONSTRAINT [PK_Sales] PRIMARY KEY CLUSTERED
(
[SalesId] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]
--Here's the sales table adding a column called description between SalesId & Month
BEGIN TRANSACTION
SET QUOTED_IDENTIFIER ON
SET ARITHABORT ON
SET NUMERIC_ROUNDABORT OFF
SET CONCAT_NULL_YIELDS_NULL ON
SET ANSI_NULLS ON
SET ANSI_PADDING ON
SET ANSI_WARNINGS ON
COMMIT
BEGIN TRANSACTION
GO
CREATE TABLE dbo.Tmp_Sales
(
SalesId int NOT NULL IDENTITY (1, 1),
Description varchar(MAX) NULL,
Month int NOT NULL,
Year int NOT NULL,
InvoiceAmount decimal(15, 2) NOT NULL,
SalesRepId int NOT NULL,
BranchId int NOT NULL
) ON [PRIMARY]
TEXTIMAGE_ON [PRIMARY]
GO
SET IDENTITY_INSERT dbo.Tmp_Sales ON
GO
IF EXISTS(SELECT * FROM dbo.Sales)
EXEC('INSERT INTO dbo.Tmp_Sales (SalesId, Month, Year, InvoiceAmount, SalesRepId, BranchId)
SELECT SalesId, Month, Year, InvoiceAmount, SalesRepId, BranchId FROM dbo.Sales WITH (HOLDLOCK TABLOCKX)')
GO
SET IDENTITY_INSERT dbo.Tmp_Sales OFF
GO
DROP TABLE dbo.Sales
GO
EXECUTE sp_rename N'dbo.Tmp_Sales', N'Sales', 'OBJECT'
GO
ALTER TABLE dbo.Sales ADD CONSTRAINT
PK_Sales PRIMARY KEY CLUSTERED
(
SalesId
) WITH( STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
GO
COMMIT