The Rambam in Hilchos Teshuvah 1:1 tells us that saying vidui (confessing) is an integral part of the teshuva process:
כָּל מִצְוֹת שֶׁבַּתּוֹרָה בֵּין עֲשֵׂה בֵּין לֹא תַּעֲשֶׂה אִם עָבַר אָדָם עַל אַחַת מֵהֶן בֵּין בְּזָדוֹן בֵּין בִּשְׁגָגָה כְּשֶׁיַּעֲשֶׂה תְּשׁוּבָה וְיָשׁוּב מֵחֶטְאוֹ חַיָּב לְהִתְוַדּוֹת לִפְנֵי הָאֵל בָּרוּךְ הוּא שֶׁנֶּאֱמַר (במדבר ה ו) "אִישׁ אוֹ אִשָּׁה כִּי יַעֲשׂוּ" וְגוֹ' (במדבר ה ז) "וְהִתְוַדּוּ אֶת חַטָּאתָם אֲשֶׁר עָשׂוּ" זֶה וִדּוּי דְּבָרִים. וִדּוּי זֶה מִצְוַת עֲשֵׂה. כֵּיצַד מִתְוַדִּין. אוֹמֵר אָנָּא הַשֵּׁם חָטָאתִי עָוִיתִי פָּשַׁעְתִּי לְפָנֶיךָ וְעָשִׂיתִי כָּךְ וְכָךְ וַהֲרֵי נִחַמְתִּי וּבֹשְׁתִּי בְּמַעֲשַׂי וּלְעוֹלָם אֵינִי חוֹזֵר לְדָבָר זֶה. וְזֶהוּ עִקָּרוֹ שֶׁל וִדּוּי. וְכָל הַמַּרְבֶּה לְהִתְוַדּוֹת וּמַאֲרִיךְ בְּעִנְיָן זֶה הֲרֵי זֶה מְשֻׁבָּח וְכֵוּ'
All the commandments of the Torah, whether mandatory or prohibitive, if a person violates any one of them, either on purpose or by accident, when he repents and returns from his sinful ways, he is obligated to confess before Hashem, as it is said: "When a man or woman shall commit any sin..… Then they shall confess their sin which they have done (Num. 5.6–7), which is a confession of words. Such confession is a positive commandment. How is the verbal confession made? The sinner says: "I beseech Thee, O Great Name! I have sinned; I have been obstinate; I have committed profanity against Thee, particularly in doing thus and such. Now, behold! I have repented and am ashamed of my actions; forever will I not relapse into this thing again." This is the essence form of teshuvah; but whosoever elaborates in confessing and extends this subject is, indeed, praise-worthy.
With this in mind (and since he can't verbalize it) is it possible for a mute person to do teshuva?