$\small \color {brown} {\text {For Blender version 3.1 with Node Wrangler}}$
The short answer is Ctrl-T which is the shortcut for the command Add Texture Setup
. But this works only if you installed the Node Wrangler plugin, it's not part of Blender itself.
Node wrangler shortcuts can be found in the documentation and in the plugin setup. In addition certain operations are directly accessible using the right panel in the shader editor area, including the one you're looking for. This menu can also be accessed using the Node Wrangler contextual menu which shortcut is Shift-W.
Last but not least, provided you know the name, as any other command it can be found in the search box displayed by Spacebar, entering a portion of add texture setup
:

(Now you can access all the plugin commands and their shortcuts, you may be interested in using some other, like Swap Links
(Alt-S) which can swap to inputs, e.g. on a Math node.
Details follow if you're interested.
Plugin setup in User Preferences
Go to user preferences, search the plugin and open Hotkey List section
:

In this section, among tens of shortcuts, you'll find:

Using the documentation
From the same user preferences page, click on the related link, which reaches this page (varies with Blender version):

Note this command Add Texture Setup
is smart enough to work both on the texture node and on the shader node.
In the right panel of the shader editor
When installing Node Wrangler plugin, a tab is added to the right panel (sidebar) of the editor. This panel can be shown / hidden by the shortcut N or using the area menu View|Sidebar
:

Using the Node Wrangler menu shortcut
The same menu can be displayed using the menu shortcut Shift-W in the shader editor.
The other Add Texture command
Node Wrangler also offers Add Principled Setup
which shortcut is Shift-Ctrl-T. It can be used with a principled shader node to add different textures at the same time, along with the coordinate mapping:

This command is not documented (at the time of the writing, the plugin online documentation is not up to date for 3.1 anyway). However from the code it is possible to see textures are associated to Principled BSDF shader using pre-defined substrings in the texture name:
name='Base Color',
default='diffuse diff albedo base col color',
description='Naming Components for Base Color maps'
name='Subsurface Color',
default='sss subsurface',
description='Naming Components for Subsurface Color maps'
name='Metallic',
default='metallic metalness metal mtl',
description='Naming Components for metallness maps'
name='Specular',
default='specularity specular spec spc',
description='Naming Components for Specular maps'
name='Normal',
default='normal nor nrm nrml norm',
description='Naming Components for Normal maps'
name='Bump',
default='bump bmp',
description='Naming Components for bump maps'
name='Roughness',
default='roughness rough rgh',
description='Naming Components for roughness maps'
name='Gloss',
default='gloss glossy glossiness',
description='Naming Components for glossy maps'
name='Displacement',
default='displacement displace disp dsp height heightmap',
description='Naming Components for displacement maps'