Here in the 1837 edition the direct object pronoun it was removed from before the complementizing that-clause. This change may have been intentional, although Joseph Smith, in his editing for the 1837 edition, did not mark this deletion in the printer’s manuscript. The direct object it here probably refers to “the sword of his justice” that is mentioned earlier in the verse—that is, the sword of God’s justice “shall overtake you”, as in Old Testament references to the sword overtaking one:
But as Don Brugger points out (personal communication), the it could also refer to “that day” as overtaking one, as in one of Paul’s epistles:
Under either antecedent, in English we expect such a direct object it to be followed by an infinitival complement rather than by a that-clause—in other words, something like “he will cause it to soon overtake you”. However, examples of a direct object followed by a complementizing that-clause for the verb cause do occur in the Book of Mormon; and in each case the subject of the that- clause is a pronoun which refers to the preceding direct object of the verb cause:
None of these other examples have it as the direct object for cause, but note that in four cases the direct object is a pronoun which is then repeated (but in a different form, in accord with standard English) as the subject in the that-clause, thus “cause us that we” and “causing them that they”. In other words, we have examples that are equivalent to the original text in 3 Nephi 29:4, yet only one of these other examples has been edited (namely, the one in 2 Nephi 5:17). The problem with the 3 Nephi 29:4 example may have been the repetition of the it. Another possibility is that the direct object it was interpreted as an expletive it and thus considered unnecessary. Yet the original text is not difficult to understand. The original construction is characteristic of the Book of Mormon text and will be restored here in 3 Nephi 29:4.
Summary: Restore the original text in 3 Nephi 29:4 with its repeated it: “he will cause it that it shall soon overtake you”; this kind of clausal construction for the verb cause is found fairly frequently elsewhere in the text, although not in this precise form.