One thing you can do is base current carrying ability of a solid pin on the same data as a solid conductor, or wire of the same size, using a chart like this:
https://xtronics.com/reference/wire_gauge-ampacity.htm
This will only tell you what the pin itself is capable of carrying, not what the socket or the connection as a whole is able to sustain.
For connectors, many factors can come into play, such as the surface area of the mating connection. For example, a pin contact may use very thin leafs of metal in the matching socket, reducing the capacity of the part. It is always best to consult the manufacturers catalog ( often available on the internet ) for the exact data.
If a connection is overloaded, the point of connection will heat up due to its resistance. This heating can lead to increased resistance, aggravating the problem, until the connection fails. Generally, connectors made to carry appreciable current are made in such a way to avoid this problem, by using secure mechanical / electrical means of mating, with adequate surface contact.
Low current connectors are often made with pins that are large enough to withstand the forces applied to insert them, or join wires to them, but their size is not always a good indicator of their current carrying ability. Often the sizes of the pieces are for mechanical or practical reasons only.
Most manufactures of connectors will list what the current capacity of their connectors are, if the part is designed to be used as a "power" connector.
If the part is intended to be used mainly as a "small-signal" or data type plug, only a voltage rating may be given, or other factors that would be related to this intended use, such as mating resistance, capacitance, etc, things that may effect its operation when used that way.