How can I run chroot on Android?
Binaries can't be executed on /sdcard because it's an emulated filesystem with fixed file permissions, mounted with noexec mount option. Create alpine directory on some other filesystem e.g. /data:

~# mkdir -p /data/local/tmp/alpine/bin


Place your executable in newly created directory and do chroot:

~# cd /data/local/tmp
~# chmod 0755 alpine/bin/busybox
~# chroot alpine /bin/busybox sh


This will drop you to a root shell (UID 0) with changed root (/).