diff --git a/Library/Homebrew/dev-cmd/audit.rb b/Library/Homebrew/dev-cmd/audit.rb
index 1a3749ca63..b27a74dcc2 100644
--- a/Library/Homebrew/dev-cmd/audit.rb
+++ b/Library/Homebrew/dev-cmd/audit.rb
@@ -887,11 +887,6 @@ module Homebrew
         # TODO: check could be in RuboCop
         problem "Use pkgshare instead of (share#{Regexp.last_match(1)}\"#{formula.name}\")"
       end
-
-      return unless @core_tap
-
-      # TODO: check could be in RuboCop
-      problem "`env :std` in homebrew/core formulae is deprecated" if line.include?("env :std")
     end
 
     def audit_reverse_migration
diff --git a/Library/Homebrew/rubocops/text.rb b/Library/Homebrew/rubocops/text.rb
index c41fd4c913..eec390e5c9 100644
--- a/Library/Homebrew/rubocops/text.rb
+++ b/Library/Homebrew/rubocops/text.rb
@@ -79,6 +79,12 @@ module RuboCop
           find_method_with_args(body_node, :go_resource) do
             problem "`go_resource`s are deprecated. Please ask upstream to implement Go vendoring"
           end
+
+          return unless formula_tap == "homebrew-core"
+
+          find_method_with_args(body_node, :env, :std) do
+            problem "`env :std` in homebrew/core formulae is deprecated"
+          end
         end
       end
     end
diff --git a/Library/Homebrew/test/.rubocop_todo.yml b/Library/Homebrew/test/.rubocop_todo.yml
index 18986235db..59e8c081af 100644
--- a/Library/Homebrew/test/.rubocop_todo.yml
+++ b/Library/Homebrew/test/.rubocop_todo.yml
@@ -21,7 +21,7 @@ RSpec/InstanceVariable:
     - 'utils/git_spec.rb'
     - 'version_spec.rb'
 
-# Offense count: 74
+# Offense count: 75
 RSpec/MultipleDescribes:
   Exclude:
     - 'ENV_spec.rb'
@@ -94,6 +94,7 @@ RSpec/MultipleDescribes:
     - 'rubocops/class_spec.rb'
     - 'rubocops/formula_desc_spec.rb'
     - 'rubocops/lines_spec.rb'
+    - 'rubocops/text_spec.rb'
     - 'rubocops/urls_spec.rb'
     - 'software_spec_spec.rb'
     - 'tap_spec.rb'
diff --git a/Library/Homebrew/test/rubocops/text_spec.rb b/Library/Homebrew/test/rubocops/text_spec.rb
index 561ff18f9e..b464f7ef51 100644
--- a/Library/Homebrew/test/rubocops/text_spec.rb
+++ b/Library/Homebrew/test/rubocops/text_spec.rb
@@ -228,3 +228,20 @@ describe RuboCop::Cop::FormulaAudit::Text do
     end
   end
 end
+
+describe RuboCop::Cop::FormulaAuditStrict::Text do
+  subject(:cop) { described_class.new }
+
+  context "When auditing formula text" do
+    it "when deprecated `env :std` is present in homebrew-core" do
+      expect_offense(<<~RUBY, "/homebrew-core/")
+        class Foo < Formula
+          url "https://brew.sh/foo-1.0.tgz"
+
+          env :std
+          ^^^^^^^^ `env :std` in homebrew/core formulae is deprecated
+        end
+      RUBY
+    end
+  end
+end