Some tests of reading do not require the child to speak.
There are tests and subtests that measure reading skills in children who are nonverbal.
Lindamood Auditory Conceptualization Test (LAC-3) will measure phonemic awareness.
Tests of Reading Comprehension (TORC-4), Relational Vocabulary Subtest measures reading vocabulary.
Diagnostic Assessment of Reading, (DAR-2), Silent Reading Comprehension subtest, will measure reading comprehension for grades 3+.
Gray Silent Reading Tests (GSRT) measure reading comprehension.
Test of Silent Contextual Reading Fluency (TOSCRF-2), Test of Silent Reading Efficiency and Comprehension (TOSREC), and Test of Silent Word Reading Fluency (TOSWRF-2) measure reading fluency. These tests measure fluency, they do not measure accuracy.
Test of Orthographic Competence (TOC) measures knowledge of letters, abbreviations, punctuation, and spelling.
Any test of spelling will provide information about a child's skill with phonics.
For a complete list of Tests that Measure Reading Skills in Nonverbal Children turn to page 63 in Wrightslaw: All About Tests and Assessments, 2nd Edition.