Dynamic Creation of Table using Stored Procedure Without a Use of OpenRowSet in SQL Server
If you cannot use OPENROWSET, you could create a loopback linked server and use OPENQUERY or EXECUTE AT.

DECLARE @srv nvarchar(4000);
SET @srv = @@SERVERNAME; -- gather this server name

-- Create the linked server
EXEC master.dbo.sp_addlinkedserver
@server     = N'LOOPBACK',
@srvproduct = N'SQLServ', -- it’s not a typo: it can’t be “SQLServer”
@provider   = N'SQLNCLI', -- change to SQLOLEDB for SQLServer 2000
@datasrc    = @srv;


-- Set the authentication to "current security context"
EXEC master.dbo.sp_addlinkedsrvlogin
@rmtsrvname  = N'LOOPBACK',
@useself     = N'True',
@locallogin  = NULL,
@rmtuser     = NULL,
@rmtpassword = NULL;


I blogged about it some years ago. 

Another option is using some kind of CLR trickery to interpret the result set definition and create a target table based on the type and length of the columns. 

If you're not allowed to use OPENROWSET, I highly doubt you will be allowed to use CLR, though. In this case, a third option could be using sp_describe_first_result_set and code your table creation script in T-SQL. It requires SQL Server 2012 or newer.