I can't assure you that I can complete the job by this month.
Please check it.
kumenglish I can't assure you that I can complete the job by this month. "by this month" is unclear. "by the end of the/this month" is better, assuming that's what you mean.
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kumenglishI can't assure you that I can complete the job by this month.
"by this month" is unclear. "by the end of the/this month" is better, assuming that's what you mean.
At the start of the sentence, "I can't promise you that I will be able to ~" reads better to me, but your wording is not actually wrong.