diff --git a/contrib/Dockerfile.test b/contrib/Dockerfile.test
index 500aff8d0..eeb6fb4e5 100644
--- a/contrib/Dockerfile.test
+++ b/contrib/Dockerfile.test
@@ -36,7 +36,7 @@ RUN apt-get update && apt-get install -y \
     libseccomp-dev \
   --no-install-recommends
 
-COPY script/setup/install-runc install-runc
+COPY script/setup/runc-version script/setup/install-runc ./
 # Allow overriding the version of runc to install through build-args
 ARG RUNC_VERSION
 ARG GOPROXY=direct
diff --git a/docs/RUNC.md b/docs/RUNC.md
index 2f35a2ce4..281c4b302 100644
--- a/docs/RUNC.md
+++ b/docs/RUNC.md
@@ -3,13 +3,13 @@ provided by [runc](https://github.com/opencontainers/runc).
 
 Development (`-dev`) and pre-releases of containerd may depend features in `runc`
 that have not yet been released, and may require a specific runc build. The version
-of runc that is tested against in our CI can be found in the `RUNC_VERSION` variable
-in the [`script/setup/install-runc`](../script/setup/install-runc) script, which
-may point to a git-commit (for pre releases) or tag in the runc repository.
+of runc that is tested against in our CI can be found in the [`script/setup/runc-version`](../script/setup/runc-version)
+file, which may point to a git-commit (for pre releases) or tag in the runc
+repository.
 
 For regular (non-pre-)releases of containerd releases, we attempt to use released
 (tagged) versions of runc. We recommend using a version of runc that's equal to
-or higher than the version of runc described in [`script/setup/install-runc`](../script/setup/install-runc).
+or higher than the version of runc described in [`script/setup/runc-version`](../script/setup/runc-version).
 
 If you encounter any runtime errors, make sure your runc is in sync with the
 commit or tag provided in that file.
diff --git a/script/setup/install-runc b/script/setup/install-runc
index 35d9ca146..7717cb1fa 100755
--- a/script/setup/install-runc
+++ b/script/setup/install-runc
@@ -21,8 +21,10 @@
 set -eu -o pipefail
 
 function install_runc() {
-	# When updating RUNC_VERSION, consider updating the runc module in go.mod as well
-	: "${RUNC_VERSION:=v1.0.0-rc93}"
+	script_dir="$(cd -- "$(dirname -- "$0")" > /dev/null 2>&1; pwd -P)"
+
+	# When updating runc-version, consider updating the runc module in go.mod as well
+	: "${RUNC_VERSION:=$(cat "${script_dir}/runc-version")}"
 
 	TMPROOT=$(mktemp -d)
 	git clone https://github.com/opencontainers/runc.git "${TMPROOT}"/runc
diff --git a/script/setup/runc-version b/script/setup/runc-version
new file mode 100644
index 000000000..e989c7fe6
--- /dev/null
+++ b/script/setup/runc-version
@@ -0,0 +1 @@
+v1.0.0-rc93