vatican.va/archive/ENG1104/_INDEX.HTM
Canons 1008 to 1054 are all about the requirements for ordination, irregularities and impairments.
From the link:
Can. 597 §1. Any Catholic endowed with a right intention who has the qualities required by universal and proper law and who is not prevented by any impediment can be admitted into an institute of consecrated life.
Can. 641 The right to admit candidates to the novitiate belongs to major superiors according to the norm of proper law.
Can. 642 With vigilant care, superiors are only to admit those who, besides the required age, have the health, suitable character, and sufficient qualities of maturity to embrace the proper life of the institute. This health, character, and maturity are to be verified even by using experts, if necessary, without prejudice to the prescript of can. 220.
Can. 643 §1. The following are admitted to the novitiate invalidly:
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§2. Proper law can establish other impediments even for validity of admission or can attach conditions.
Can. 644 Superiors are not to admit to the novitiate secular clerics without consulting their proper ordinary nor those who, burdened by debts, cannot repay them.
Can. 645 §1. Before candidates are admitted to the novitiate, they must show proof of baptism, confirmation, and free status.
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Can. 1025 §1. To confer the presbyteral or diaconal orders licitly, it is required that the candidate, having completed the period of probation according to the norm of law, is endowed in the judgment of his own bishop or of the competent major superior with the necessary qualities, is prevented by no irregularity and no impediment, and has fulfilled the prerequisites according to the norm of cann. 1033-1039. Moreover, the documents mentioned in can. 1050 are to be obtained and the investigation mentioned in can. 1051 is to be completed.
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Can. 1029 Only those are to be promoted to orders who, in the prudent judgment of their own bishop or of the competent major superior, all things considered, have integral faith, are moved by the right intention, have the requisite knowledge, possess a good reputation, and are endowed with integral morals and proven virtues and the other physical and psychic qualities in keeping with the order to be received.
As your link indicated, a deaf man can become a priest. This was not heard off in the past.
Certainly - there are always exceptions to the rule.
DD