First, how big is the current database?  What version of Access are you
using?

You might be able to do this incrementally.
-- Compact the database
-- Add a new field - number  type Long  (if your present field has no
decimal portion)
-- Run an update query that selects only a limited number of records and
updates them.

UPDATE YourTable
SET [NewNumberField] = Val([TheTextField])
WHERE [NewNumberField] Is Null and Val([TheTextField]) < = 1000

-- Check the size of the database.  Has it grown too much? If so, compact
and then repeat.

If not, then you could run something like the following in a loop in a VBA
function and check the size of your database after each iteration.  When you
approach the maximum size for an Access database then exit the loop and
compact the the database.

UPDATE YourTable
SET [NewNumberField] = Val([TheTextField])
WHERE [TheTextField] IN
   (SELECT TOP 1000 [TheTextField]
    FROM YourTable
    WHERE [NewNumberField] is NULL
    ORDER BY [TheTextField])

If you can't construct the necessary VBA, post back.

How big is the MDB currently? (and what version of Access are you using?)

Access 2000 and newer does not support an MDB file of larger than 2 Gb
(Access 97 and earlier only support 1 Gb). If you're close to that, then
you're not going to be able to make the necessary change in your database.
What you could try doing is creating a new database and linking to the table
in your existing database. In the new database, create a copy of the table
(no data) with the numeric field rather than the text field. Write an Append
query (INSERT INTO) that takes the data from the linked table and populates
the new table. Once you know that table is okay, go back into your original
database, delete the table, then import the new table in.