漢字の読み方はおろか
Can I also say
漢字を読むのはおろか
Do they have the same meaning?
Basically, 疎{おろ}か is an adjective (形容動詞) so it has to "decorate" a noun. In Japanese a nominalized sentence just behave like a noun so both of your sentences are grammatical and make sense. But their meaning is slighly different.
漢字{かんじ}の読{よ}み方{かた}はおろか,...
Not to mention the way kanji are read, ...
Whereas,
漢字{かんじ}を読{よ}むのはおろか,...
Not to mention (the fact of) reading kanji, ...
The provided translations are not deemed to be perfect since the omitted part ,the part after おろか, is even more important that what comes before in order to translate properly.
Other examples can be found in the second link (see below).
References:
Although it may depend on the context, I would basically say 'no'. The two phrases mean different things and because of that, one would expect different types of phrases to follow each. The two would largely be uninterchangeable.
「[漢字]{かんじ}の[読]{よ}み[方]{かた}はおろか」 would mean "not to mention how to read (the) kanji", "not to mention how (the) kanji are read", etc.
A phrase like 「カタカナの読み方さえ知らない」 would most naturally (and logically) follow, making the whole sentence mean:
"Not to mention how to read kanji, (someone) does not even know how to read katakana."
「漢字を読むのはおろか」 would mean "not to mention reading kanji". Unlike the first phrase, this one can be followed by a phrase that has nothing to do with reading.
A phrase like 「かんたんなフレーズさえ[声]{こえ}に[出]{だ}して[練習]{れんしゅう}しようとしない」 would best follow.
"Let alone reading kanji, (someone) does not try to practice even the simple phrases out loud."