Here is, what I think, a better solution than what @Adem posted.
Java:
java
try {
// https://github.com/android/platform_frameworks_base/blob/kitkat-release/core/java/android/widget/TextView.java#L562-564
Field f = TextView.class.getDeclaredField("mCursorDrawableRes");
f.setAccessible(true);
f.set(yourEditText, R.drawable.cursor);
} catch (Exception ignored) {
}
XML:
xml
<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android"
android:shape="rectangle" >
<solid android:color="#ff000000" />
<size android:width="1dp" />
</shape>