Set shiftwidth to 4 spaces to mtach the tabstop. This will make indenting the same as tabbing.

.vimrc

@@ -1,12 +1,13 @@
 " Vim settings
-set tabstop =4	" The amount of spaces per tab
-syntax on 		" Syntax highlighting
-set number		" Line numbers
-set cursorline	" Shows a line on the cursor's line
+set tabstop =4		" The amount of spaces per tab
+set shiftwidth =4 	" The amount of spaces when shifting >> <<
+syntax on 			" Syntax highlighting
+set number			" Line numbers
+set cursorline		" Shows a line on the cursor's line
 
 " Search settings
-set incsearch	" Search as characters are entered
-set hlsearch	" Highlight all matches
+set incsearch		" Search as characters are entered
+set hlsearch		" Highlight all matches
 
 " Changes colorcolumn per line that hits 81 characters
 call matchadd('ColorColumn', '\%81v', 100)