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diff --git a/src/arrow/r/tests/testthat/test-compute-sort.R b/src/arrow/r/tests/testthat/test-compute-sort.R
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+++ b/src/arrow/r/tests/testthat/test-compute-sort.R
@@ -0,0 +1,155 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+library(dplyr, warn.conflicts = FALSE)
+
+# randomize order of rows in test data
+tbl <- slice_sample(example_data_for_sorting, prop = 1L)
+
+test_that("sort(Scalar) is identity function", {
+  int <- Scalar$create(42L)
+  expect_equal(sort(int), int)
+  dbl <- Scalar$create(3.14)
+  expect_equal(sort(dbl), dbl)
+  chr <- Scalar$create("foo")
+  expect_equal(sort(chr), chr)
+})
+
+test_that("Array$SortIndices()", {
+  int <- tbl$int
+  # Remove ties because they could give non-deterministic sort indices, and this
+  # test compares sort indices. Other tests compare sorted values, which are
+  # deterministic in the case of ties.
+  int <- int[!duplicated(int)]
+  expect_equal(
+    Array$create(int)$SortIndices(),
+    Array$create(order(int) - 1L, type = uint64())
+  )
+  # Need to remove NAs because ARROW-12063
+  int <- na.omit(int)
+  expect_equal(
+    Array$create(int)$SortIndices(descending = TRUE),
+    Array$create(rev(order(int)) - 1, type = uint64())
+  )
+})
+
+test_that("ChunkedArray$SortIndices()", {
+  int <- tbl$int
+  # Remove ties because they could give non-deterministic sort indices, and this
+  # test compares sort indices. Other tests compare sorted values, which are
+  # deterministic in the case of ties.
+  int <- int[!duplicated(int)]
+  expect_equal(
+    ChunkedArray$create(int[1:4], int[5:length(int)])$SortIndices(),
+    Array$create(order(int) - 1L, type = uint64())
+  )
+  # Need to remove NAs because ARROW-12063
+  int <- na.omit(int)
+  expect_equal(
+    ChunkedArray$create(int[1:4], int[5:length(int)])$SortIndices(descending = TRUE),
+    Array$create(rev(order(int)) - 1, type = uint64())
+  )
+})
+
+test_that("sort(vector), sort(Array), sort(ChunkedArray) give equivalent results on integers", {
+  compare_expression(
+    sort(.input),
+    tbl$int
+  )
+  compare_expression(
+    sort(.input, na.last = NA),
+    tbl$int
+  )
+  compare_expression(
+    sort(.input, na.last = TRUE),
+    tbl$int
+  )
+  compare_expression(
+    sort(.input, na.last = FALSE),
+    tbl$int
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE),
+    tbl$int,
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = TRUE),
+    tbl$int,
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = FALSE),
+    tbl$int,
+  )
+})
+
+test_that("sort(vector), sort(Array), sort(ChunkedArray) give equivalent results on strings", {
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = FALSE),
+    tbl$chr
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = FALSE),
+    tbl$chr
+  )
+})
+
+test_that("sort(vector), sort(Array), sort(ChunkedArray) give equivalent results on floats", {
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = TRUE),
+    tbl$dbl
+  )
+  compare_expression(
+    sort(.input, decreasing = FALSE, na.last = TRUE),
+    tbl$dbl
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = NA),
+    tbl$dbl
+  )
+  compare_expression(
+    sort(.input, decreasing = TRUE, na.last = FALSE),
+    tbl$dbl,
+  )
+  compare_expression(
+    sort(.input, decreasing = FALSE, na.last = NA),
+    tbl$dbl
+  )
+  compare_expression(
+    sort(.input, decreasing = FALSE, na.last = FALSE),
+    tbl$dbl,
+  )
+})
+
+test_that("Table$SortIndices()", {
+  x <- Table$create(tbl)
+  expect_identical(
+    as.vector(x$Take(x$SortIndices("chr"))$chr),
+    sort(tbl$chr, na.last = TRUE)
+  )
+  expect_identical(
+    as.data.frame(x$Take(x$SortIndices(c("int", "dbl"), c(FALSE, FALSE)))),
+    tbl %>% arrange(int, dbl)
+  )
+})
+
+test_that("RecordBatch$SortIndices()", {
+  x <- record_batch(tbl)
+  expect_identical(
+    as.data.frame(x$Take(x$SortIndices(c("chr", "int", "dbl"), TRUE))),
+    tbl %>% arrange(desc(chr), desc(int), desc(dbl))
+  )
+})