There is no functionality within The Raiser's Edge to merge or combine attributes.  One Attribute will need to be deleted and the data added to the records using the other attribute.  This is best done using an Export and an Import.

First, you'll need to locate the records that have the specific Attribute you want to delete.  For this example, we will use a Constituent Attribute.
1. Create a Query of Constituents that have the Attribute Category. NOTE: you must type in the value for the Attribute Category, it is NOT a drop down or selection option

Query Criteria Attribute Category
2. Save and close that query
3. Go to Export and create a new Constituent export to a Comma Delimited Format and include the query created above
4. Add the Constituent Import ID to the output
5. Select the Attribute Description, Comments and Date  in the Output for the specific Attribute you want to delete (NOTE: you will enter a 1 or MORE if records have more than 1 of the specific Attribute you want to delete)
For this example we're using Interests as the Attribute selected.

Attribute Export Options
6. Your final Output will look like this (you may use either Import ID or Constituent ID in your output)
Export One Options

7. Export this file and Open the CSV file
8. Insert a column in front of the Attribute Description and give it this header CAttrCat
9. Change the column headers to the following:
ImportID
ConsID
CAttrCat -- populate this column with the desired Attribute Category (the one you are keeping)
CAttrDesc
CAttrDate
CAttrCom
10. Save this file as a CSV and close it.
11. Login to The Raiser's Edge and go to Admin>Import>Constituent>Constituent and click NEW at the top
12. Select to Update Existing records, choose how to identify existing Constituents based on Import ID or Constituent ID (choose the one you have in your file)
13. Include your CSV file by clicking the ellipses and navigating to the file (change file type from IMP to All or Text)
14. Go to the Fields tab and confirm the fields are mapped correctly
15. Import the records to make the change
16. Go to Admin>Globally Delete Records and select record type of Attribute.  More information can be found in this article