diff --git a/changelog/fix_rails_order_arguments_cop_false_positives.md b/changelog/fix_rails_order_arguments_cop_false_positives.md
new file mode 100644
index 0000000000..30867e9fc5
--- /dev/null
+++ b/changelog/fix_rails_order_arguments_cop_false_positives.md
@@ -0,0 +1 @@
+* [#1510](https://github.com/rubocop/rubocop-rails/pull/1510): Fix `Rails/OrderArguments` cop false positives when using column index argument. ([@viralpraxis][])
diff --git a/lib/rubocop/cop/rails/order_arguments.rb b/lib/rubocop/cop/rails/order_arguments.rb
index c4e14c0dfc..75f8d0bd50 100644
--- a/lib/rubocop/cop/rails/order_arguments.rb
+++ b/lib/rubocop/cop/rails/order_arguments.rb
@@ -52,6 +52,7 @@ def replacement(order_expressions)
           order_arguments.map! { |arg| extract_column_and_direction(arg.strip) }
 
           return if order_arguments.any?(&:nil?)
+          return if order_arguments.any? { |column_name, _| positional_column?(column_name) }
 
           convert_to_preferred_arguments(order_arguments).join(', ')
         end
@@ -68,6 +69,10 @@ def convert_to_preferred_arguments(order_expressions)
           end
         end
 
+        def positional_column?(column_name)
+          column_name.match?(/\A\d+\z/)
+        end
+
         def extract_column_and_direction(order_expression)
           return unless (column, direction = ORDER_EXPRESSION_REGEX.match(order_expression)&.captures)
 
diff --git a/spec/rubocop/cop/rails/order_arguments_spec.rb b/spec/rubocop/cop/rails/order_arguments_spec.rb
index 74b451df73..6e9227dc01 100644
--- a/spec/rubocop/cop/rails/order_arguments_spec.rb
+++ b/spec/rubocop/cop/rails/order_arguments_spec.rb
@@ -128,4 +128,30 @@
       User.order('LEFT(first_name, 1)')
     RUBY
   end
+
+  context 'with numeric string literal column name' do
+    it 'does not register an offense for `order` with a string argument' do
+      expect_no_offenses(<<~RUBY)
+        User.order('1')
+      RUBY
+    end
+
+    it 'does not register an offense for `order` with multiple string arguments' do
+      expect_no_offenses(<<~RUBY)
+        User.order('1', 'last_name')
+      RUBY
+    end
+
+    it 'does not registers an offense for `order` with a string argument with DESC direction' do
+      expect_no_offenses(<<~RUBY)
+        User.order('1 DESC')
+      RUBY
+    end
+
+    it 'does not register an offense for `order` with a string argument with ASC order' do
+      expect_no_offenses(<<~RUBY)
+        User.order('1 ASC')
+      RUBY
+    end
+  end
 end