Step 1: Understanding the Concept:
The question asks to identify the political movement associated with the famous slogan by Bal Gangadhar Tilak.
Step 2: Detailed Explanation:
The powerful slogan, "Swaraj is my birthright and I shall have it" (Swarajya is my birthright and I shall have it), was given by the nationalist leader Bal Gangadhar Tilak. He used this slogan extensively to mobilize the Indian masses during the Home Rule Movement (1916-1918). The movement, led by Tilak and Annie Besant, aimed to achieve self-government or 'home rule' for India under the British Empire. This slogan became the cornerstone of the movement's ideology, emphasizing the natural right of Indians to govern themselves.
Step 3: Final Answer:
The slogan is associated with the Home Rule Movement.