Language certificates when applying to positions in the USA I am non-US citizen and I want to apply for an academic position in the USA.

At which point do I need to show up a language certificate? For example, together with the job application, or together with the visa application?
Normally TOEFL is required for admissions in USA. However, you must check the requirements that are required by the University first to secure admission that may or may not include TOEFL beside other tests such as GRE, GRE subject, GAT etc.

Second is the visa requirements, make sure if the TOEFL is required or not for the visa, as in that case, you may get admission but denied visa or vice versa. so get eligibility criteria from different universities, compare them and find out what are the common requirements for all the universities, and then check the visa requirements.

Time of showing language certificate depend on the university, they can ask in advance or later.