In Ayodhya Kanda, Sita, while narrating her marriage episode to Anasuya, wife of Sage Atri, states that Janaka himself received a great bow from Varuna, the god of Water (rain-god), but not from Lord Shiva.
महा यज्ने तदा तस्य वरुणेन महात्मना |
दत्तम् धनुर् वरम् प्रीत्या तूणी च अक्षय्य सायकौ || (Ayodhya Kanda 118th Sarga 39th Sloka)
In ancient days, Janaka on the occasion of a great sacrifice, received with affection from Varuna (वरुणेन महात्मना) the rain-god, an excellent bow with two quivers that should never lack arrows.
असंचाल्यम् मनुष्यैः च यत्नेन अपि च गौरवात् |
तन् न शक्ता नमयितुम् स्वप्नेषु अपि नर अधिपाः || (Ayodhya Kanda 118th Sarga 40th Sloka)
That bow was so heavy in weight that no man could lift it up nor any of the kings were bale to bend it even in their dreams.
तच् च दृष्ट्वा धनुः श्रेष्ठम् गौरवाद् गिरि सम्निभम् |
अभिवाद्य नृपा जग्मुर् अशक्ताः तस्य तोलने || २-११८-४३
Seeing that excellent bow, resembling a mountain in weight, and being unable to lift it up, the princes offered salutation to it and went away.
सुदीर्घस्य तु कालस्य राघवो अयम् महा द्युतिः |
विश्वामित्रेण सहितो यज्नम् द्रष्टुम् समागतः || २-११८-४४
लक्ष्मणेन सह भ्रात्रा रामः सत्य पराक्रमः |
After a very long time, this Rama born in Raghu dynasty with a great splendour possessing a true valour, along with his brother Lakshmana together with a sage Visvamitra, came to witness a sacrifice.
इत्य् उक्तः तेन विप्रेण तद् धनुः समुपानयत् || २-११८-४७
निमेष अन्तर मात्रेण तद् आनम्य स वीर्यवान् |
ज्याम् समारोप्य झटिति पूरयाम् आस वीर्यवान् || २-११८-४८
Hearing the words of Vivamitra, Janaka caused the bow to be brought there. The mighty and the valiant Rama bent that bow merely within an instant and immediately stringed the bow with the bow-cord and drew the bow to the full.
Now, the question is, whose bow did Sri Rama actually break? The prevalent story is Sri Rama broke Shiva's bow.