This can be achieved by using the "program functions" that are assignable to system permission groups. There are 4 program functions that deal with the transport functions.
You have to assign the functions to a custom system group and assign your system user to the group. By default the functions to use the Transporter are assigned to the system group "VID_Features".
Please refer to the
Configuration guide, Availability of Certain Functionality for further information.
For more information on editing system user and permissions group permissions, please refer to the Configuration guide, Working with the User & Permissions Group Editor.
Using the Database Transporter requires that you do have the function group (aka features) in your permission list:
Transport_Export
Transport_Import
Transport_SnapShot
Transport_SQL
Every function group is assigned to at least one permissions group which your person/account in Identity Manager is assigned to or not.
In Designer select the Permissions tab then "Program functions" for a list of features and the assignment to permission groups (the "Permissions groups" tab is available at the bottom of the screen):

In order to have less impact, you could define a new permissions group and assign only those functions (features) which are required. The new permissions group must be linked to the system user.