dialing

No — say "I am dialing his number". Dial is transitive and takes the number or person as a direct object without the preposition 'to'.

Definition

v. to enter a phone number by pressing buttons or turning a wheel to make a call.

v. the present participle of 'dial'; refers to the act of entering a series of digits into a telephone to establish a connection.

simple

“She is dialing the emergency number right now.”

contextual

“I spent ten minutes dialing the office, but the line was busy every time I tried.”

Transitive or intransitive; can be used with or without a direct object (the number).

I am dialing to him

I am dialing his number

Dial is transitive and takes the number or person as a direct object without the preposition 'to'.