Yes, you can sort alphabetically in Word Tables.
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On the Help menu of the program, click the first item in the list, such as "View Help," "Help Topics," or a similar phrase. (This text will vary.)
– or –
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I have Windows Vista. These are the instructions at Word Help Tables
Sort the contents of a table
In Print Layout view (Print Layout view: A view of a document or other object as it will appear when you print it. For example, items such as headers, footnotes, columns, and text boxes appear in their actual positions.), move the pointer over the table until the table move handle appears.
Click the table move handle to select the table that you want to sort.
Under Table Tools, on the Layout tab, in the Data group, click Sort.
In the Sort dialog box, select the options that you want.
Sort a single column in a table
Select the column that you want to sort.
Under Table Tools, on the Layout tab, in the Data group, click Sort.
Under My list has, click Header row or No header row.
Click Options.
Under Sort options, select the Sort column only check box.
Click OK.
Sort by more than one word or field inside a table column
To sort the data in a table that is based on the contents of a column that includes more than one word, you must first use characters to separate the data — including data in the header row. For example, if the cells in a column contain both last and first names, you can use commas to separate the names.
Select the column that you want to sort.
Under Table Tools, on the Layout tab, in the Data group, click Sort.
Under My list has, click Header row or No header row.
Click Options.
Under Separate fields at, click the type of character that separates the words or fields that you want to sort, and then click OK.
Under Sort by, in the Using list, select which word or field you want to sort by.
In the first Then by list, enter the column that contains the data that you want to sort by, and then in the Using list, select which word or field you want to sort by.
If you want to sort by an additional column, repeat this step in the second Then by list.