Can Prednisone cause ringing/humming in the ears?

Yes it can in some instances. Prednisone has all kinds of potential side effects. Here is some information from Drugs.com.

Side Effects of Prednisone - for the Consumer
Prednisone
All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome when using Prednisone:

Difficulty sleeping; feeling of a whirling motion; increased appetite; increased sweating; indigestion; mood changes; nervousness.

Seek medical attention right away if any of these SEVERE side effects occur when using Prednisone:
Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue); appetite loss; black, tarry stools; changes in menstrual periods; convulsions; depression; diarrhea; dizziness; exaggerated sense of well-being; fever; general body discomfort; headache; increased pressure in the eye; joint or muscle pain; mood swings; muscle weakness; personality changes; prolonged sore throat, cold, or fever; puffing of the face; severe nausea or vomiting; swelling of feet or legs; unusual weight gain; vomiting material that looks like coffee grounds; weakness; weight loss.

Prednisone Concentrate
All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome when using Prednisone Concentrate:

Difficulty sleeping; feeling of a whirling motion; increased appetite; increased sweating; indigestion; mood changes; nervousness.

Seek medical attention right away if any of these SEVERE side effects occur when using Prednisone Concentrate:
Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue); appetite loss; black, tarry stools; changes in menstrual periods; convulsions; depression; diarrhea; dizziness; exaggerated sense of well-being; fever; general body discomfort; headache; increased pressure in the eye; joint or muscle pain; mood swings; muscle weakness; personality changes; prolonged sore throat, cold, or fever; puffing of the face; severe nausea or vomiting; swelling of feet or legs; unusual weight gain; vomiting material that looks like coffee grounds; weakness; weight loss.

Prednisone Solution
All medicines may cause side effects, but many people have no, or minor, side effects. Check with your doctor if any of these most COMMON side effects persist or become bothersome when using Prednisone Solution:

Difficulty sleeping; feeling of a whirling motion; increased appetite; increased sweating; indigestion; mood changes; nervousness.

Seek medical attention right away if any of these SEVERE side effects occur when using Prednisone Solution:
Severe allergic reactions (rash; hives; itching; difficulty breathing; tightness in the chest; swelling of the mouth, face, lips, or tongue); appetite loss; black, tarry stools; changes in menstrual periods; convulsions; depression; diarrhea; dizziness; exaggerated sense of well-being; fever; general body discomfort; headache; increased pressure in the eye; joint or muscle pain; mood swings; muscle weakness; personality changes; prolonged sore throat, cold, or fever; puffing of the face; severe nausea or vomiting; swelling of feet or legs; unusual weight gain; vomiting material that looks like coffee grounds; weakness; weight loss.